Differential Equations · Mathematics · AP EAPCET

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MCQ (Single Correct Answer)

1
The differential equation of the family of hyperbols having their centres at origin and their axes along coordinates axes is
AP EAPCET 2024 - 22th May Evening Shift
2

The general solution of the differential equation $\left(x y+y^2\right) d x-\left(x^2-2 x y\right) d y=0$ is

AP EAPCET 2024 - 22th May Evening Shift
3
The general solution of the differential equation $(1+\tan y)(d x-d y)+2 x d y=0$ is
AP EAPCET 2024 - 22th May Morning Shift
4
The general solution of the differential equation $x d y-y d x=\sqrt{x^2+y^2} d x$ is
AP EAPCET 2024 - 22th May Morning Shift
5

The sum of the order and degree of differential equation $x\left(\frac{d^2 y}{d x^2}\right)^{1 / 2}=\left(1+\frac{d y}{d x}\right)^{4 / 3}$

AP EAPCET 2024 - 22th May Morning Shift
6
The differential equation formed by eliminating arbitrary constants $A, B$ from the equation $y=A \cos 3 x+B \sin 3 x$ is
AP EAPCET 2024 - 21th May Evening Shift
7
If $\cos x \frac{d y}{d x}-y \sin x=6 x,\left(0 < x < \frac{\pi}{2}\right)$ and $y\left(\frac{\pi}{3}\right)=0$, then $y\left(\frac{\pi}{6}\right)=$
AP EAPCET 2024 - 21th May Evening Shift
8

$\frac{d y}{d x}=\frac{y+x \tan \frac{y}{x}}{x} \Rightarrow \sin \frac{y}{x}=$

AP EAPCET 2024 - 21th May Evening Shift
9
The differential equation formed by eliminating $a$ and $b$ from the equation $y=a e^{2 x}+b x e^{2 x}$ is
AP EAPCET 2024 - 21th May Morning Shift
10
If $y=a^3 e^{y^2 x+c}$ is the general solution of a differential equation, where $a$ and $c$ are arbitrary constants and $b$ is fixed constant, then the order of differential equation is
AP EAPCET 2024 - 21th May Morning Shift
11
The solution of differential equation $\left(x+2 y^3\right) \frac{d y}{d x}=y$ ls
AP EAPCET 2024 - 21th May Morning Shift
12
Order and degree of the differential equation $\frac{d^3 y}{d x^3}=\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{5}{2}}$, respectively are
AP EAPCET 2024 - 20th May Evening Shift
13
Integrating factor of the differential equation $\sin x \frac{d y}{d x}-y \cos x=1$ is
AP EAPCET 2024 - 20th May Evening Shift
14
The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x$ is
AP EAPCET 2024 - 20th May Evening Shift
15
The sum of the order and degree of the differential equation $\frac{d^4 y}{d x^4}=\left\{c+\left(\frac{d y}{d x}\right)^2\right\}^{3 / 2}$ is
AP EAPCET 2024 - 20th May Morning Shift
16

$$ \begin{aligned} &\text { The general solution of the differential equation }\\ &(x+y) y d x+(y-x) x d y=0 \text { is } \end{aligned} $$

AP EAPCET 2024 - 20th May Morning Shift
17
The general solution of the differential equation $\left(y^2+x+1\right) d y=(y+1) d x$ is
AP EAPCET 2024 - 20th May Morning Shift
18
The difference of the order and degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^{-\frac{7}{2}}\left(\frac{d^3 y}{d x^3}\right)^2-\left(\frac{d^2 y}{d x^2}\right)^{-\frac{5}{2}}\left(\frac{d^4 y}{d x^4}\right)=0$ is
AP EAPCET 2024 - 19th May Evening Shift
19
If $x d y+\left(y+y^2 x\right) d x=0$ and $y=1$ at $x=1$, then
AP EAPCET 2024 - 19th May Evening Shift
20
The solution of $x d y-y d x=\sqrt{x^2+y^2} d x$ when $y(\sqrt{3})=1$ is
AP EAPCET 2024 - 19th May Evening Shift
21
The differential equation representing the family of circles having their centres of Y -axis is $\left(y_1=\frac{d y}{d x}\right.$ and $\left.y_2=\frac{d^2 y}{d x^2}\right)$
AP EAPCET 2024 - 18th May Morning Shift
22
The general solution of the differential equation $\left(\sin y \cos ^2 y-x \sec ^2 y\right) d y=(\tan y) d r$, is
AP EAPCET 2024 - 18th May Morning Shift
23
The general solution of the differential equation $(x-y-1) d y=(x+y+1) d x$ is
AP EAPCET 2024 - 18th May Morning Shift
24

The general solution of the differential equation $$\frac{d y}{d x}=\cos ^2(3 x+y)$$ is $$\tan ^{-1}\left(\frac{\sqrt{3}}{2} \tan (3 x+y)\right)=f(x)$$. Then, $$f(x)=$$

AP EAPCET 2022 - 5th July Morning Shift
25

If the general solution of the differential equation $$\cos ^2 x \frac{d y}{d x}+y=\tan x$$ is $$y=\tan x-1+C e^{-\tan x}$$ satisfies $$y\left(\frac{\pi}{4}\right)=1$$, then $$C=$$

AP EAPCET 2022 - 5th July Morning Shift
26

Assertion (A) Order of the differential equations of a family of circles with constant radius is two.

Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.

AP EAPCET 2022 - 5th July Morning Shift
27

If $$l$$ and $$m$$ are order and degree of a differential equation of all the straight lines at constant distance of $$P$$ units from the origin, then $$l m^2+l^2 m=$$

AP EAPCET 2022 - 4th July Evening Shift
28

If $$2 x-y+C \log (|x-2 y-4|)=k$$ is the general solution of $$\frac{d y}{d x}=\frac{2 x-4 y-5}{x-2 y+2}$$, then $$C=$$

AP EAPCET 2022 - 4th July Evening Shift
29

By eliminating the arbitrary constants from $$y=(a+b) \sin (x+c)-d e^{x+e+f}$$, then differential equation has order of

AP EAPCET 2022 - 4th July Evening Shift
30

If the solution of $$\frac{d y}{d x}-y \log _e 0.5=0, y(0)=1$$, and $$y(x) \rightarrow k$$, as $$x \rightarrow \infty$$, then $$k=$$

AP EAPCET 2022 - 4th July Morning Shift
31

$$y=A e^x+B e^{-2 x}$$ satisfies which of the following differential equations?

AP EAPCET 2022 - 4th July Morning Shift
32

The solution of the differential equation $$2x\left(\frac{dy}{dx}\right)-y=4$$ represents a family of

AP EAPCET 2021 - 20th August Morning Shift
33

The solution of the differential equation $$\frac{d^2 y}{d x^2}+y=0$$ is

AP EAPCET 2021 - 19th August Morning Shift
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