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Differential Equations Concepts for JEE

13+ syllabus-aligned questions available

Quick answer

Master Differential Equations by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

Build clear conceptual foundations for Differential Equations before speed practice. This guide covers what JEE expects and how to test yourself with MCQs.

Concept explainer

Concept overview for Differential Equations covering 3 JEE syllabus subtopics including Ordinary differential equations, their order and degree, The solution of differential equation by the method of separation of variables, Solution of a homogeneous and linear differential equation of the type dy/dx + p(x)y = q(x).

Key points

  • Understand the definition and scope of Ordinary differential equations, their order and degree in the JEE syllabus
  • Memorise key formulas and standard results linked to Ordinary differential equations, their order and degree
  • Practise 20–40 syllabus-aligned MCQs with step-by-step solutions
  • Understand the definition and scope of The solution of differential equation by the method of separation of variables in the JEE syllabus
  • Memorise key formulas and standard results linked to The solution of differential equation by the method of separation of variables
  • Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

  • Revise Ordinary differential equations, their order and degree with a one-page formula sheet before attempting mixed tests
  • After each practice set, log mistakes specific to Ordinary differential equations, their order and degree and reattempt after 48 hours
  • Revise The solution of differential equation by the method of separation of variables with a one-page formula sheet before attempting mixed tests
  • After each practice set, log mistakes specific to The solution of differential equation by the method of separation of variables and reattempt after 48 hours

Common trap

Students often rush Ordinary differential equations, their order and degree questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

JEE Formula Sheet

36+ important formulas for Differential Equations

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Subtopics in Differential Equations

View Differential Equations formula sheet — 36+ JEE formulas

Free sample questions

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Q1MathsUnit 9: Differential Equations
The order, degree of the differential equation satisfying the relation 1+x2+1+y2=λ(x1+y2)\sqrt{1+x^{2}}+\sqrt{1+y^{2}}=\lambda(x \sqrt{1+y^{2}}) y1+x2)\left.y \sqrt{1}+x^{2}\right) is
Q2MathsUnit 9: Differential Equations
The family of curves represented by dy1dx=x2+x+1y2+y+1\frac{d y_{1}}{d x}=\frac{x^{2}+x+1}{y^{2}+y+1} and the family represented by dy2dx+y2+y+1x2+x+1=0\frac{\boldsymbol{d} \boldsymbol{y}_{2}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\boldsymbol{y}^{2}+\boldsymbol{y}+\mathbf{1}}{\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}}=\mathbf{0}
Q3MathsUnit 9: Differential Equations
The order and degree of the differential equation, (d2ydx2)3=sin⁡y+3x\left(\frac{d^{2} y}{d x^{2}}\right)^{3}=\sin y+3 x \quad are
Q4MathsUnit 9: Differential Equations
Solution of the differential equation tan⁡y⋅sec⁡2xdx+tan⁡x⋅sec⁡2ydy=0\tan y \cdot \sec ^{2} x d x+\tan x \cdot \sec ^{2} y d y=0 is
Q5MathsUnit 9: Differential Equations
(1−xy+x2y2)dx=x2dy\left(1-x y+x^{2} y^{2}\right) d x=x^{2} d y
Q6MathsUnit 9: Differential Equations
The order and degree of the differential equation. (d2ydx2)3+(dydx)=∫ydx\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d y}{d x}\right)=\int y d x are respectively.
Q7MathsUnit 9: Differential Equations
The normal at any point P(x,y)\boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) of a\mathbf{a} curve meets the xx -axis at QQ and NN is the foot of the ordinate at PP If NQ=x(1+y2)1+x2,N Q=\frac{x\left(1+y^{2}\right)}{1+x^{2}}, then equation of such curve, given that it passes through the point (3,1) is:
Q8MathsUnit 9: Differential Equations
Assertion A normal is drawn at a point P(x,y)\boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) of a\mathbf{a} curve. It meets the xx -axis and the yy -axis in point AA and BB, respectively, such that 1OA+1OB=1,\frac{1}{O A}+\frac{1}{O B}=1, where OO is the origin. The equation of such a curve passing through (5,4)(\mathbf{5}, \mathbf{4}) is (x−1)2+(x-1)^{2}+ (y−1)2=25(y-1)^{2}=25 Reason OA=x+ydydx\boldsymbol{O A}=\boldsymbol{x}+\boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} and OB=x+ydydxdydx\boldsymbol{O} \boldsymbol{B}=\frac{\boldsymbol{x}+\boldsymbol{y} \frac{d \boldsymbol{y}}{d \boldsymbol{x}}}{\frac{d \boldsymbol{y}}{d \boldsymbol{x}}}

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What concepts in Differential Equations are essential for JEE?

Focus on core ideas across Ordinary differential equations, their order and degree, The solution of differential equation by the method of separation of variables, Solution of a homogeneous and linear differential equation of the type dy/dx + p(x)y = q(x). JEE tests application, not just memorisation.

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