PrepWiser › Learn › Mathematics › Differential EquationsDifferential Equations — JEE Main PYQs & Practice Questions Differential Equations is a Mathematics chapter in the JEE Main syllabus. This page brings together 202 previous-year and practice questions on Differential Equations, organised into 4 topics: Order and Degree, Variable Separable Method, Linear Differential Equations and Homogeneous Equations. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Order and Degree Variable Separable Method Let dy/dx = (ax - by + a)/(bx + cy + a), a,b,c ∈ R, represents a circle with center (α… The general solution of the differential equation √(1 + x² + y² + x²y²) + xydy/dx = 0 is… Let y=y(x) be a solution curve of the differential equation. (1-x² y²) d x=y d x+x d y… Let y=y(x) be the solution of the differential equation (x+y+2)² d x=d y, y(0)=-2. Let… Let the solution curve x=x(y), 0 < y < π/2, of the differential equation (log ₑ(cos y))²… If the solution curve f(x, y)=0 of the differential equation (1+log ₑ x) (d x)/(d y)-x… A hostel has 100 students. On a certain day (consider it day zero) it was found that two… Let y = y(x) be the solution of the differential equation dy/dx = 1 + xeʸ⁻ˣ, - √2 < x <… Let y = y(x) be solution of the differential equation log ( dy/dx ) = 3x + 4y, with y(0)… The differential equation satisfied by the system of parabolas y² = 4a(x + a) is : Let y = y(x) be the solution of the differential equation, (2 + sin x)/(y + 1).dy/dx = -… Let x=x(y) be the solution of the differential equation 2y²dx/dy-2xy+x²=0, y>1, x(e)=e… Let y=y(x) be the solution of the differential equation (d y)/(d x)=2 x(x+y)³-x(x+y)-1… Let the tangent at any point P on a curve passing through the points (1, 1) and (1/10… Let y = y(x) be the solution curve of the differential equation dy/dx = y/x( 1 + xy²(1 +… Let the solution curve of the differential equation xdy-ydx=√(x²+y²)dx,x>0, y(1)=0, be… If y = y(x) is the solution of the differential equation ( 1 + e²ˣ )dy/dx + 2( 1 + y²… If the solution y=y(x) of the differential equation (x⁴+2 x³+3 x²+2 x+2) d y-(2 x²+2… If the solution curve y=y(x) of the differential equation (1+y²)(1+log ₑ x) d x+x d y=0… Let y=y(x) be the solution of the differential equation dy/dx=(1+x+x²)(1-y+y²),y(0)=1/2… Linear Differential Equations If a curve passes through the origin and the slope of the tangent to it at any point (x… Let f be a differentiable function such that 2(x+2)² f(x)-3(x+2)²=10 ∫₀ˣ(t+2) f(t) d t… Let x=x(t) and y=y(t) be solutions of the differential equations (d x)/dt+a x=0 and (d… Let y = y(x) be the solution of the differential equation (1 - x²)dy = ( xy + (x³ +… If y = y(x) is the solution of the differential equation, dy/dx + 2y tan x = sin x,y(… Let g be a differentiable function such that ∫₀ˣ g(t) d t=x-∫₀ˣ tg(t) d t, x ≥ 0 and let… Let the solution y=y(x) of the differential equation (d y)/(d x)-y=1+4 sin x satisfy… Let the solution curve y=y(x) of the differential equation (d y)/(d x)-(3 x⁵ tan… Let y=y(x) be the solution of the differential equation (2 x log ₑ x) (d y)/(d x)+2… Let y=y(x) be the solution of the differential equation sec xdy/dx-2y=2+3 sin x, x∈… If y=y(x) is the solution of the differential equation (d y)/(d x)+2 y=sin (2 x)… If y=y(x) is the solution of the differential equation (d y)/(d x)+(4 x)/(x²-1)… Let y = y(x) be the solution of the differential equation cosxdy/dx + 2ysinx = sin2x, x… If y=y(x), x ∈(0, π / 2) be the solution curve of the differential equation (sin ² 2 x)… Let f:[1,∞)→ R be a differentiable function defined as f(x)=∫₁ˣf(t)dt+(1-x)(logₑ x-1)+e… For a differentiable function f: ℝ → ℝ, suppose f′(x)=3 f(x)+α, where α ∈ ℝ, f(0)=1 and… If xφ (x) = ∫₅ˣ (3t² - 2φ '(t))dt, x > -2, and φ(0) = 4, then φ(2) is __________. Let y = y(x) be the solution of the differential equation cos x(3 sin x + cos x + 3)dy =… Let y = y(x), x > 1, be the solution of the differential equation (x - 1)dy/dx + 2xy =… If y = y(x) is the solution curve of the differential equation x²dy + ( y - 1/x )dx = 0… Homogeneous Equations Let x = x(y) be the solution of the differential equation 2y e^(x/y²)dx + ( y² -… Let y = y(x) be the solution of the differential equation x tan ( y/x )dy = ( y tan (… Let C₁ be the curve obtained by the solution of differential equation 2xydy/dx = y² -… If ydy/dx = x[ y²/x² + (φ ( y²/x² ))/(φ '( y²/x² )) ], x > 0, φ > 0, and y(1) = -1, then… If y = y(x) is the solution of the differential equation 2x²dy/dx - 2xy + 3y² = 0 such… The solution of the differential equation (d y)/(d x)=-((x²+3 y²)/(3 x²+y²)), y(1)=0 is : If sin (y/x)=log ₑ|x|+α/2 is the solution of the differential equation x cos (y/x) (d… If the solution curve of the differential equation (d y)/(d x)=(x+y-2)/(x-y) passes… Suppose the solution of the differential equation (d y)/(d x)=((2+α) x-β y+2)/(β x-2 α… If dy/dx = xy/(x² + y²); y(1) = 1; then a value of x satisfying y(x) = e is : Let the solution curve of the differential equation xdy/dx - y = √(y² + 16x²), y(1) = 3… If a curve y = f(x), passing through the point (1, 2), is the solution of the… The solution of the differential equation (x²+y²) d x-5 x y d y=0, y(1)=0, is : Let the solution curve y = y(x) of the differential equation [ x/√(x² - y²) + e^(y/x)… If the solution curve y = y(x) of the differential equation y²dx + (x² - xy + y²)dy = 0… Let the solution curve of the differential equation x d y=(√(x²+y²)+y) d x, x>0… Let y = y(x) be the solution of the differential equation xdy - ydx = √(x² - y²) dx, x ≥… If the curve, y = y(x) represented by the solution of the differential equation (2xy² -… Let y=y(x) be the solution of the differential equation (x²-3y²)dx+3xy dy=0,y(1)=1. Then… Let y=y(x) be the solution of the differential equation (d y)/(d x)=(4 y³+2 y x²)/(3 x… More Mathematics chapters Frequently asked questions How many Differential Equations questions are there for JEE Main? PrepWiser has 202 Differential Equations questions for JEE Main, grouped into 4 topics such as Order and Degree, Variable Separable Method and Linear Differential Equations.
Are these Differential Equations questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Differential Equations questions? Open any Differential Equations question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.