Mathematics · JEE

Ordinary differential equations, their order and degree Concepts for JEE

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Concept explainer

Ordinary differential equations, their order and degree is a core JEE Main Mathematics subtopic under Differential Equations. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

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

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

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.

Syllabus context

Part of Differential Equations in JEE Main Mathematics.

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

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.

Q5MathsUnit 9: Differential Equations

Assertion The order of the differential equation, of which

\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

x \frac{d^{2} y}{d x^{2}}+

2 \frac{d y}{d x}-x y+x^{2}-2=0

Q6MathsUnit 9: Differential Equations

The differential equation corresponding to

x y=c^{2},

where

c

is an arbitrary constant, is:

Q7MathsUnit 9: Differential Equations

Order and degree of

\left(x^{2}+2 x\right) y_{2}^{2}+\left(x^{2}-2\right) y_{1}^{3}-2(x+

\mathbf{3}) \boldsymbol{y}=\mathbf{0}

are:

Q8MathsUnit 9: Differential Equations

Consider the following statements: 1. The general solution of

\frac{d y}{d x}=f(x)+

x

is of the form

y=g(x)+c,

where

c

is an arbitrary constant. 2. The degree of

\left(\frac{d y}{d x}\right)^{2}=f(x)

is 2 Which of the above statements is/are correct?

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