DIFFERENTIAL EQUATIONS JEE Mains Super 40 Revision Series
JEE Mains Super 40 Revision SeriesDIFFERENTIAL EQUATIONS Download Doubtnut TodayQues No.QuestionJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS1 6742Solve the differential equation xdydx y(log y log x 1). Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe solution of the differential equation (12 102602) ke (tan 1y)(2)2xe (2tan 1y)xe (2tan 1y) e (tan 1y) k 2 y ) (x etan 1y)(dy)/(dx) 0,is(1)(x e (2tan 1y) k(3)xe (tan 1y) tan 1y k(4) Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe differential equation of all circles passing through the origin and having their centreson the x axis is (1)3 11414(4) y 2 x2x2 y2dy xydx(2)x2 ydy 2xydx Watch Free Video Solution on Doubtnut2dy 3xydx(3)y2 x2dy 2xydx
4 11418JEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe normal to a curve at P (x, y) meets the x axis at G. If the distance of G from theorigin is twice the abscissa of P, then the curve is a (1) ellipse (2) parabola (3) circle (4)hyperbola Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS5 11460The differential equation of the family of circles with fixed radius 5 units and centre on the22line y 2 is (1) (x 2)y'2 25 (y 2) (2) (y 2)y'2 25 (y-2) (3)(y 2)2y'2 25 (y 2)2(4) (x 2)2y'2 25 (y 2)2 Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS6 11469The differential equation which represents the family of curves y 2c1 andc2 are arbitrary constants, is (1) y' y(2) y' ' y' y (3)yy' ' (y' )c1 e, where y' (4)c2 xyy' '2 Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe population p(t) at time t of a certain mouse species satisfies the differential equationdp(t)7 11561dt 0. 5p(t) 450Ifp(0) 850becomes zero is (1) 2 ln 18 (2) ln 9 (3)1, then the time at which the populationIn 18 (4) ln 182 Watch Free Video Solution on Doubtnut8 11664JEE Mains Super 40 Revision Series DIFFERENTIAL tion
dy(x log x)dx y 2x log x, (x 1)Then y(e) is equal to : (1) e (2) 0 (3) 2 (4) 2e Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS9 14300If y(t) is solution of (tdy 1)dx ty 1, y(0) 1then y(1) Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSSolution of differential equation10 14312y f (x) cey cf (x) e(2)xy dyf (x)dx (f (x)) f (x) cex(3)2is : (1) f (x)y f (x)' . yy (4)x f (x) ce f (x)x Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe general solution of the differential equationdyx y sin(dx11 17354is(a)ylog tan(ylog tan(π ) C 2 sin x)22ylog tan(2) C 2 sin x2(b)x y) sin(x) C 2 sin(4(c))2(d) Non of these4 Watch Free Video Solution on Doubtnut12 19690JEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSIf (243dy sin x)(3)13dx(4) 23 (y 1)cos x 0andπy(0) 1, theny()2is equal to1 3(2)
Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe differential equation representing the family of curves y 2c(x c), whereis a positive parameter, is of (a) order 1 (b) order 2 (c) degree 3 (d) degree 4213 35267c Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSA normal atP (x, y)on a curve meets the x axis atQandNis the foot of the ordinate214 35278at P . If N Qx(1 y ) 1 x2, then the equation of curve given that it passes through thepoint (3, 1) is Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS15 35286Orthogonal trajectories of family of the curvearbitrary constant, is22x3 y3 a(23), whereais any Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS16 35290Tangent to a curve intercepts the y axis at a point P A line perpendicular to this tangentthrough P passes through another point (1, 0). The differential equation of the curve is Watch Free Video Solution on Doubtnut17 35316JEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe differential equation for the family of curvearbitrary constant, isx2 y2 2ay 0,whereais an
Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS18 35319Ifdydx (ey x) 1,where y(0) 0, then y is expressed explicitly as Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS19 35331The solution of the differential equation (2dy)dy xdx y 0isdx Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSA curve20 35333passes through point P (1, 1) . The normal to the curve at P is a(y 1) (x 1) 0 . If the slope of the tangent at any point on the curve isproportional to the ordinate of the point, then the equation of the curve isy f (x) Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS21 35339For the primitive integral equationy( 3) is (a) 3 (b) 2 (c) 1 (d) 52ydx y dy xdy; x R, y 0, y(1) 1,then Watch Free Video Solution on Doubtnut22 35341JEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe solution of the primitive integral equationy(1) 1and y(x0 ) e,then x0 is(x22 y )dy xydxisy y(x).If
Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSπA curve passes through the point23 35344(x, y)beyxx). Let the slope of the curve at each point6y sec((1,), x 0.Then the equation of the curve is Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe differential equation 1 y 2dy dx24 35345determines a family of circle with (a) variableyradii and a fixed centre at(0, 1) (b) variable radii and a fixed centre at (0, 1)(c) Fixedradius 1 and variable centres along the x axis. (d) Fixed radius 1 and variable centresalong the y axis. Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSAcurvepassingthrough(2, 3)andsatisfyingthedifferentialequationx25 353532 ty(t)dt x y(x), (x 0)is0 Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS26 35368Differential equation of the family of curvesAv constants, is Watch Free Video Solution on Doubtnutr B,whereAandBare arbitrary
27 35371JEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThesolutiondyx 1 xyof2x y dx2dy(the2)3x y differentialequation3dy(dx2!3) .isdx3! Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS28 35386The solution of the equation log (dy) ax byisdx Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS29 35434If integrating factor ofequal to223x(1 x )dy (2x y y ax )dx 0ise pdx ,thenPis Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS30 35959Find the value ofstraight linesλif2x2 7xy 3y2 8x 14y λ 0represents a pair of Watch Free Video Solution on Doubtnut31 70368JEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSSolutionoftheequation2dyx()dy (y x)dx(B)(x 2y c)(xy c) 0(x y c)(2xy c) 0(d) (x y 0is(A)dx(x y c)(xy c) 0 y c)(xy c) 0(C)
Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSSolution32 93872ofthedifferentialsec y x 1 cer(b) sec ydyequationsin y x 1 cedx(c) yr cos y(1 x cos y) x eris(a) c Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSdxSolution of the differential equation33 324745xx ryey(B) ey xey(C) x yedyyxI nxe 1 I nx(D) yyif exy(1) 0is (A)1 I nxy Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSLet34 1241925bey g(x)thesolutiondysin x() y cos x 4x, x (0, π)ofIf y(dxtheπ) 0differential, then y(2π)equationis equal to6 Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSdyThe solution of the differential equation35 14633241y x2b. x1 y2c. x1 yd. ydx2y 1 x Watch Free Video Solution on Doubtnutx 0withy(1) 1is given by a.
JEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSSolution of the differential equation36 1463331b. x(y cos x) sin x Cdydxc. x(yy x sin xis a.x(y cos x) sin x C cos x) cos x Cd. None of these Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe37 1463346tantansolution 1 1of 1x tany tan 1thedifferentialy tanx tan 1CCd.tanequationb. 12dy(1 x )tany tan 1 1dxy tanx tan 1 y 1 12is 0,x tan 1a.c.CC Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe38 2843751solutionofx yf (x) cthedifferential(B) x. f 1 (x)equation, c 0(C) y dyf (x) x cdxis f ' (x)y 1(A)(d) non of thesef (x) Watch Free Video Solution on DoubtnutJEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSThe39 2993499solutionofthedifferential2is (a) sec xc (d) Non of thesecos y log(sec x tan x)dx cos x log(sec y tan y)dy(b) sec x sec y c(c) sec x sec y Watch Free Video Solution on Doubtnutequation sec2y c
JEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONSA curve satisfies the differential equationdyx 1 xy dx40 3394197(0, 0)(1) The equation of the curve iscurve is x ytangent to curve222 2x 2y x y2x2(3) y22and passes throughx y y22 2x x yx 02(2) The equation of theis a tangent to curve (4)y 0is a Watch Free Video Solution on Doubtnut Download Doubtnut to Ask Any Math Question By just a click Get A Video Solution For Free in Seconds Doubtnut Has More Than 1 Lakh Video Solutions Free Video Solutions of NCERT, RD Sharma, RS Aggarwal, Cengage(G.Tewani), Resonance DPP, Allen, Bansal, FIITJEE, Akash, Narayana,VidyaMandir Download Doubtnut Today
DIFFERENTIAL EQUATIONS Download Doubtnut Today Ques No. Question 1 6742 JEE Mains Super 40 Revision Series DIFFERENTIAL EQUATIONS Solve the differential equation . Watch Free Video Solution on Doubtnut 2 10260 JEE Mains Super 40
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8. JEE (MAIN) 2015 Candidates who wish to appear in JEE (Advanced) 2015 must write Paper-1 of JEE (Main) 2015 which is likely to be held in the month of April 2015. Candidates may visit the website www.jeemain.nic.in for information about JEE (Main) 2015. 9. ELIGIBILITY CRITERIA FOR APPEARING IN JEE (ADVANCED) 2015
(iii) introductory differential equations. Familiarity with the following topics is especially desirable: From basic differential equations: separable differential equations and separa-tion of variables; and solving linear, constant-coefficient differential equations using characteristic equations.
Andhra Pradesh State Council of Higher Education w.e.f. 2015-16 (Revised in April, 2016) B.A./B.Sc. FIRST YEAR MATHEMATICS SYLLABUS SEMESTER –I, PAPER - 1 DIFFERENTIAL EQUATIONS 60 Hrs UNIT – I (12 Hours), Differential Equations of first order and first degree : Linear Differential Equations; Differential Equations Reducible to Linear Form; Exact Differential Equations; Integrating Factors .
3 Ordinary Differential Equations K. Webb MAE 4020/5020 Differential equations can be categorized as either ordinary or partialdifferential equations Ordinarydifferential equations (ODE's) - functions of a single independent variable Partial differential equations (PDE's) - functions of two or more independent variables
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Chapter 1 Introduction 1 1.1 ApplicationsLeading to Differential Equations 1.2 First Order Equations 5 1.3 Direction Fields for First Order Equations 16 Chapter 2 First Order Equations 30 2.1 Linear First Order Equations 30 2.2 Separable Equations 45 2.3 Existence and Uniqueness of Solutionsof Nonlinear Equations 55
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