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Important Questions: Differential Equations for JEE

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The most important Differential Equations questions for JEE cover conceptual traps, standard results, and numerical patterns from 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). Goodmarks provides 7+ high-yield MCQs with full solutions.

Focus on what matters most. These important Differential Equations questions cover high-weightage concepts from 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) — the topics JEE repeats every year.

Subtopics in Differential Equations

  • 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)

Free sample questions

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Q1MathsUnit 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
Q2MathsUnit 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}}}
Q3MathsUnit 9: Differential Equations
Assertion The order of the differential equation, of which xy=cex+be−x+x2\boldsymbol{x} \boldsymbol{y}=\boldsymbol{c} \boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{b} \boldsymbol{e}^{-\boldsymbol{x}}+\boldsymbol{x}^{\boldsymbol{2}} is a solution, is 2 Reason The differential equation is xd2ydx2+x \frac{d^{2} y}{d x^{2}}+ 2dydx−xy+x2−2=02 \frac{d y}{d x}-x y+x^{2}-2=0
Q4MathsUnit 9: Differential Equations
The differential equation corresponding to xy=c2,x y=c^{2}, where cc is an arbitrary constant, is:
Q5MathsUnit 9: Differential Equations
Order and degree of (x2+2x)y22+(x2−2)y13−2(x+\left(x^{2}+2 x\right) y_{2}^{2}+\left(x^{2}-2\right) y_{1}^{3}-2(x+ 3)y=0\mathbf{3}) \boldsymbol{y}=\mathbf{0} are:
Q6MathsUnit 9: Differential Equations
Consider the following statements: 1. The general solution of dydx=f(x)+\frac{d y}{d x}=f(x)+ xx is of the form y=g(x)+c,y=g(x)+c, where cc is an arbitrary constant. 2. The degree of (dydx)2=f(x)\left(\frac{d y}{d x}\right)^{2}=f(x) is 2 Which of the above statements is/are correct?
Q7MathsUnit 9: Differential Equations
A certain radioactive material is known to decay at a rate proportional to the amount present. If after one hour it is observed that 10 percent of the material has decayed, find the half-life (period of time it takes for the amount of material to decrease by half) of the material (in hrs.)

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Frequently asked questions

What makes a Differential Equations question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

Which subtopics in Differential Equations are high-weightage?

Key areas include 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). Prioritise these before moving to edge cases.

How many important questions should I revise?

Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

Can I practise only important questions on Goodmarks?

Pro users can filter by unit and subtopic to target high-yield areas. Free users can attempt sample questions on this page.

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