Differential Equations PYQs - Last 10 Years

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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 25 of 75 filtered questions.

1Differential Equations

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

2Differential Equations

If $x d y+\left(y+y^2 x\right) d x=0$ and $y=1$ at $x=1$, then

3Differential Equations

The solution of $x d y-y d x=\sqrt{x^2+y^2} d x$ when $y(\sqrt{3})=1$ is

4Differential Equations

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

5Differential Equations

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

6Differential Equations

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

7Differential Equations

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 $\left.y_2=\frac{d^2 y}{d x^2}\right)$

8Differential Equations

If $\frac{d y}{d x}=f(x, y)$ is a homogeneous differential equation, then the general form of $f(x, y)$ is

9Differential Equations

The substitution $x=v y$ converts which one of the following differential equation to an equation solvable by variable separable method?

10Differential Equations

The order and degree of the differential equation $\left(\frac{d^3 y}{d x^3}\right)^{\frac{1}{2}}-2\left(\frac{d y}{d x}\right)^{\frac{1}{4}}+x y=0$ are respectively

11Differential Equations

If $x^\alpha \frac{d y}{d x}=y^\beta(\gamma \log x+\delta \log y+1)$ is a homogeneous differential equation, then

12Differential Equations

The general soluiton of the differential equation $\tan x \tan y d x+\cos ^2 x \operatorname{cosec}^2 y d y=0$ is

13Differential Equations

If $\alpha$ and $\beta$ are respectively, the order and degree of the differential equation $y=e^{\left(\frac{d y}{d x}+\frac{d^2 y}{d x^2}\right)}$, then the value of $\alpha+\alpha^\beta+\alpha^{2 \beta}+\ldots+\alpha^{2023 \beta}=$

14Differential Equations

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.

15Differential Equations

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 \(C=\)

16Differential Equations

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, \(f(x)=\)

17Differential Equations

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

18Differential Equations

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 \(k=\)

19Differential Equations

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 \(C=\)

20Differential Equations

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

21Differential Equations

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 \(l m^2+l^2 m=\)

22Differential Equations

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

23Differential Equations

The equation of the curve passing through the point \(\left(0, \frac{\pi}{4}\right)\) and satisfying the differential equation \(\left(e^x \tan y\right) d x\left.+\left(1+e^x\right) \sec ^2 y\right) d y=0\) is given by

24Differential Equations

If \(y=\sin (\sin x)\) and \(y^{\prime \prime}+f(x) \cdot y^{\prime}+g(x) \cdot y=0\), then \(f(x) \cdot g(x)\) is equal to

25Differential Equations

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