Differential Equations - Gujarat Board (GSEB) STD 12 Science Maths Questions

The degree of the differential equation $\left(\frac{d s}{d t}\right)^4+3 s \frac{d^2 s}{d t^2}=0$ is :

The degree of the differential equation $x y \frac{d^2 y}{d x^2}+x\left(\frac{d y}{d x}\right)^3-y \frac{d y}{d x}=0$ is :

A
3
✓
1
C
$0$
D
2

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark

The degree of differential equation $\sqrt{1+\left(\frac{d y}{d x}\right)^2}=$ $a\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{3}}:$

A
1
✓
2
C
3
D
4

Answer: B.

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Q 4M.C.Q (1 Marks)1 Mark

The solution of the equation $\frac{d y}{d x}=\frac{1-\cos 2 y}{1+\cos 2 y}$ is :

A
$x+\tan y+y=c$
B
$x+\cot y-y=c$
C
$x+\tan y-y=c$
✓
$x+\cot y+y=c$

Answer: D.

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Q 5M.C.Q (1 Marks)1 Mark

The solution of the equation $\frac{d y}{d x}=\cos ^2 y$ is :

A
$x+\tan y=c$
✓
$\tan y=x+c$
C
$\sin y+x=c$
D
$\sin y-x=c$

Answer: B.

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Q 61 Marks1 Mark

How many number of arbitrary constants in the general solution of a differential equation of fourth order.

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Q 71 Marks1 Mark

Write the integrating factor of the equation $\frac{d y}{d x}+\frac{1}{\sin x}$ $y=e^x$.

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Q 81 Marks1 Mark

Write the general solution of the equation $\frac{d y}{d x}+\frac{1}{x} y=$ $x$.

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Q 91 Marks1 Mark

Solve : $\frac{d y}{d x}=5 x+7$

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Q 101 Marks1 Mark

What will be the differential equation of the curve $y=$ $A e^x+ B e^{-x}$ ?

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Q 112 Marks2 Marks

Find the general solution of the differential equation $\left(1+x^2\right) d y=\left(1+y^2\right) d x$.

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Q 122 Marks2 Marks

Find the solution of the following differential equation :
$
x \sqrt{1+y^2} d x+y \sqrt{1+x^2} d y=0
$

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Q 132 Marks2 Marks

For the following differential equation find the sum of its order and degree :
$
y=x\left(\frac{d y}{d x}\right)^3+\frac{d^2 y}{d x^2}
$

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Q 143 Marks3 Marks

Solve the following differential equation :
$
\left(x^2-1\right) \frac{d y}{d x}+2 x y=\frac{1}{x^2-1},|x| \neq 1
$

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Q 153 Marks3 Marks

Solve : $\cos (x+y) d y=d x$.

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Q 164 Marks4 Marks

Solve the differential equation $\frac{d y}{d x}+y \tan x=y^2$ $\sec x$.

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Q 174 Marks4 Marks

Find a particular solution of the differential equation $\frac{ dy }{ dx }+2 y \cot x=4 x \operatorname{cosec} x$ $(x \neq 0)$, given that $y=0$, when $x=\frac{\pi}{2}$.

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Q 184 Marks4 Marks

Solve the following differential equation :
$
x d y+\left(y-x^3\right) d x=0
$

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Q 194 Marks4 Marks

Solve the following differential equation :
$
y-x \frac{d y}{d x}=x+y \frac{d y}{d x}
$

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Q 204 Marks4 Marks

Solve the following differential equation :
$
\sqrt{1+x^2+y^2+x^2 y^2}+x y \frac{d y}{d x}=0
$

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Differential Equations question types

Differential Equations questions

Generate a Differential Equations paper free

Differential Equations Maths - Differential Equations

Differential Equations question types

Differential Equations questions

Generate a Differential Equations paper free