Mathematics · JEE

Differential Equations Short Tricks for JEE

13+ syllabus-aligned questions available

Quick answer

Short tricks for Differential Equations work only with strong fundamentals. Apply the tips below in timed sets and review every explanation.

Use these Differential Equations shortcuts to save time in JEE Mathematics papers — then validate speed with 13+ MCQs on Goodmarks.

Short tricks for speed

Differential Equations focus drill
Solve 15 mixed MCQs for Differential Equations, review every explanation, and note formulas you hesitated on.
Calculus substitution scan
Spot standard forms (sin²x, 1/(a²+x²), e^ax) before integrating — JEE rewards pattern recognition.
Graph sketch shortcut
For coordinate geometry, mark intercepts and asymptotes first; many MCQs need only qualitative graph features.

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Subtopics in Differential Equations

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Free sample questions

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Q1MathsUnit 9: Differential Equations

The order, degree of the differential equation satisfying the relation

\sqrt{1+x^{2}}+\sqrt{1+y^{2}}=\lambda(x \sqrt{1+y^{2}})

\left.y \sqrt{1}+x^{2}\right)

Q2MathsUnit 9: Differential Equations

The family of curves represented by

\frac{d y_{1}}{d x}=\frac{x^{2}+x+1}{y^{2}+y+1}

and the family represented by

\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,

\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 \cdot \sec ^{2} x d x+\tan x \cdot \sec ^{2} y d y=0

Q5MathsUnit 9: Differential Equations

\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.

\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

\boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y})

\mathbf{a}

curve meets the

x

-axis at

Q

and

N

is the foot of the ordinate at

P

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

\boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y})

\mathbf{a}

curve. It meets the

x

-axis and the

y

-axis in point

A

and

B

, respectively, such that

\frac{1}{O A}+\frac{1}{O B}=1,

where

O

is the origin. The equation of such a curve passing through

(\mathbf{5}, \mathbf{4})

(x-1)^{2}+

(y-1)^{2}=25

Reason

\boldsymbol{O A}=\boldsymbol{x}+\boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}

and

\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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Frequently asked questions

Are short tricks enough for Differential Equations in JEE?

No — tricks complement concepts. Master the theory first, then use shortcuts in timed MCQ practice.