Differential Equations · Mathematics · VITEEE

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MCQ (Single Correct Answer)

1

The differential equation corresponding to the family of curves $y=e^x(a x+b)$ is

VITEEE 2024
2

If $$m$$ and $$n$$ are order and degree of the question $$\left(\frac{d^2 y}{d x^2}\right)^4+8 \frac{\left(d^2 y / d x^2\right)^3}{\left(d^4 y / d x^4\right)^5}+\left(\frac{d^4 y}{d x^4}\right)=x^2+4$$, then $$m-n$$ is equal to

VITEEE 2023
3

The solution of $$d y / d x=1+x+y+x y$$ is

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4

If $$x d y / d x=x^2+y-2, y(1)=1$$, then $$y(2)$$ is equal to

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5

The solution of differential equation $$y y^{\prime}=x\left(\frac{y^2}{x^2}+\frac{f\left(y^2 / x^2\right)}{f^{\prime}\left(y^2 / x^2\right)}\right)$$ is

VITEEE 2023
6

Find the solution of equation $$\frac{d y}{d x}=\frac{1}{\cos (x+y)}$$

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7

Find the solution of $$\frac{d y}{d x}=\frac{1}{\cos (x-y)}$$

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8

The solution of the equation $$\frac{d y}{d x}+x(x+y)=x^3(x+y)^3-1$$ is

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9

If $$p$$ and $$q$$ are order and degree of the question $$\left(\frac{d^2 y}{d x^2}\right)^4+4 \frac{\left(\frac{d^2 y}{d x^2}\right)^2}{\left(\frac{d^3 y}{d x^3}\right)^3}+\frac{d^3 y}{d x^3}=x^2-1$$, then

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10

The solution of $$\frac{d y}{d x}=1+x+y+x y$$ is

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11

The general solution of the linear differential equation $$\frac{d y}{d x}+\sec x \cdot y=\tan x\left(0 \leq x \leq \frac{\pi}{2}\right)$$ is

VITEEE 2021
12

On solving the differential equation $$x^2 y d x-\left(x^3+y^3\right) d y=0$$, the value of $$\log y$$ is

VITEEE 2021
13

The particular solution of the differential equation $$\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x$$, such that $$y(\pi / 2)=0$$ is

VITEEE 2021
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