Differential Equations PYQs - Last 10 Years

AP EAPCET / Mathematics / Calculus / 75 recent questions

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All Differential Equations PYQs Last 5 Years Create chapter test

Practice 75 AP EAPCET Mathematics questions from Differential Equations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Differential Equations Questions

Showing 50 of 75 filtered questions.

1Differential Equations

If $A x^3+B x y=4$ ( $A$ and $B$ are arbitrary constants) is the general solution of the differential equation $F(x) \frac{d^2 y}{d x^2}+G(x) \frac{d y}{d x}-2 y=0$, then $F(l)+G(l)=$

2Differential Equations

The general solution of the differential equation $\cos (x+y) d y=d x$ is

3Differential Equations

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

4Differential Equations

The general solutions of the differential equation $x \log x d y=(x \log x-y) d x$ is

5Differential Equations

If $y=A t^2+\frac{B}{t}$ ( $A, B$ are parameters) is general solution of the differential equation $f(t) y^{\prime \prime}(t)+g(t) y^{\prime}(t)+h(t) y=0$ then $2 f(t)+t^2 h(t)=$

6Differential Equations

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

7Differential Equations

The general solution of the differential equation $x y(y+2) d y+\left(y^3-1\right) d x=0$ is

8Differential Equations

If $a$ and $b$ are arbitrary constants, then the differential equation corresponding to the family of curves $y=\tan (a x+b)$ is

9Differential Equations

The general solution of the differential equation $\left(1+\sin ^2 x\right) \frac{d y}{d x}+y \sin 2 x=\cos x+\sin ^2 x \cos x$ is

10Differential Equations

If the slope of the tangent drawn at any point $(x, y)$ on a curve is $(x+y)$, then the equation of that curve is

11Differential Equations

If $x \log x \frac{d y}{d x}+y=\log x^2$ and $y(e)=0$, then $y\left(e^2\right)=$

12Differential Equations

The solution of the differential equation $x^2(y+1) \frac{d y}{d x}+y^2(x+1)^2=0$, when $y(1)=2$, is

13Differential Equations

The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x+y-3}{2 y-x+3}$

14Differential Equations

The general solution of the differential equation $\sec (x-y+1) d y=d x$ is

15Differential Equations

The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x y-4 x+y-2}{2 x y+x-4 y-2}$ is

16Differential Equations

The differential equation for which $y^2=4 a(x+a)$ ( $a$ is the parameter) is the general solution is

17Differential Equations

If the order and degree of the differential equation $x \frac{d^2 y}{d x^2}=\left(1+\left(\frac{d^2 y}{d x^2}\right)^2\right)^{-1 / 2}$ are $k$ and $l$ respectively, then $k, l$ are the roots of

18Differential Equations

The general solution of the differential equation $(x-(x+y) \log (x+y)) d x+x d y=0$ is

19Differential Equations

The equation of the curve passing through the point $(0, \pi)$ and satisfying the differential equation $y d x=\left(x+y^3 \cos y\right) d y$ is

20Differential Equations

If the degree of the differential equation corresponding to the family of curves $y=a x+\frac{1}{a}$ (where $a \neq 0$ is an arbitary constant) is $r$ and it's order is $m$. Then, the solution of $\frac{d y}{d x}=\frac{y}{2 x}, y(\mathrm{l}...

21Differential Equations

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

22Differential Equations

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

23Differential Equations

The general solution of the differential equation $\frac{d y}{d x}+\frac{\sec x}{\cos x+\sin x} y=\frac{\cos x}{1+\tan x}$ is

24Differential Equations

The general solution of the differential equation $\frac{d y}{d x}=\frac{x+y}{x-y}$ is

25Differential Equations

The differential equation of the family of circles passing through the origin and having centre on $X$-axis is

26Differential Equations

The general solution of the differential equation $\frac{d y}{d x}+\frac{x+y+1}{x-3 y+5}=0$ is

27Differential Equations

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

28Differential Equations

The general solution of the differential equation $\frac{d y}{d x}+x y=4 x-2 y+8$ is

29Differential Equations

The differential equation corresponding to the family of parabolas whose axis is along $x=1$ is

30Differential Equations

The general solution of the differential equation
\(\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x\)

31Differential Equations

The general solution of the equation $\frac{d y}{d x}+\frac{1}{x} y=\frac{1}{x} e^x$

32Differential Equations

The differential equation for which $a x+b y=1$ is general solution is

33Differential Equations

Among the options given below from which option a differential equation of order two can be formed ?

34Differential Equations

The solution of the differential equation $e^x y d x+e^x d y+x d x=0$ is

35Differential Equations

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

36Differential Equations

The general solution of the differential equation $x d y-y d x=\sqrt{x^2+y^2} d x$ is

37Differential Equations

The general solution of the differential equation $(1+\tan y)(d x-d y)+2 x d y=0$ is

38Differential Equations

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

39Differential Equations

The differential equation of the family of hyperbols having their centres at origin and their axes along coordinates axes is

40Differential Equations

The solution of differential equation $\left(x+2 y^3\right) \frac{d y}{d x}=y$ ls

41Differential Equations

The differential equation formed by eliminating $a$ and $b$ from the equation $y=a e^{2 x}+b x e^{2 x}$ is

42Differential Equations

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

43Differential Equations

The differential equation formed by eliminating arbitrary constants $A, B$ from the equation $y=A \cos 3 x+B \sin 3 x$ is

44Differential Equations

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

45Differential Equations

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 $y\left(\frac{\pi}{6}\right)=$

46Differential Equations

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

47Differential Equations

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

48Differential Equations

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

49Differential Equations

Integrating factor of the differential equation $\sin x \frac{d y}{d x}-y \cos x=1$ is

50Differential Equations

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