Differential Equations PYQs - Last 10 Years

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MathematicsCalculus2017-2026

All Differential Equations PYQs Last 5 Years Create chapter test

Practice 27 KCET Mathematics questions from Differential Equations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

27

PYQs on Page

Mathematics / Calculus

2017-2026

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Based on indexed question metadata

13

Last 5 Years

2022-2026

27

Last 10 Years

2017-2026

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27PYQs

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13 in last 5 years27 in last 10 years

Last 10 Years Differential Equations Questions

Showing 27 of 27 filtered questions.

1Differential Equations

Integrating factor of the differential equation $(1 + x^2)\dfrac{dy}{dx} + xy = 1$ is

2Differential Equations

$\int xf(x)\,dx + \dfrac{f(x)}{2} = 0$, then $f(x)$ is equal to

3Differential Equations

Sum of the squares of the order and degree (if defined) of a differential equation $2 y^{\prime}+\left(y^{\prime \prime}\right)^2=\sqrt{y^{\prime \prime}-3}$ is

4Differential Equations

If ' $a$ ' and ' $b$ ' are the order and degree respectively of the differentiable equation. $\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^3+x^4=0$, then $a-b=$ $\qquad$

5Differential Equations

General solution of the differential equation $\frac{d y}{d x}+y \tan x=\sec x$ is

6Differential Equations

The solution of $e^{d y / d x}=x+1, y(0)=3$ is

7Differential Equations

The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coordinates of that point is

8Differential Equations

The degree of the differential equation \(1+\left(\frac{d y}{d x}\right)^2+\left(\frac{d^2 y}{d x^2}\right)^2=\sqrt[3]{\frac{d^2 y}{d x^2}+1}\) is

9Differential Equations

If a curve passes through the point \((1,1)\) and at any point \((x, y)\) on the curve, the product of the slope of its tangent and \(x\) coordinate of the point is equal to the \(y\) coordinate of the point, then the curve also passes thro...

10Differential Equations

The sum of the degree and order of the differential equation \(\left(l+y_1^2\right)^{2 / 3}=y_2\) is

11Differential Equations

If \(y(x)\) is the solution of differential equation \(x \log x \frac{d y}{d x}+y=2 x \log x, y(e)\) is equal to

12Differential Equations

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

13Differential Equations

If \(\frac{d y}{d x}+\frac{y}{x}=x^2\), then \(2 y(2)-y(1)=\)

14Differential Equations

Solution of differential equating \(x d y-y d x=0\) represents

15Differential Equations

The number of solutions of \(\frac{d y}{d x}=\frac{y+1}{x-1}\), when \(y(\mathrm{l})=2\) is

16Differential Equations

The curve passing through the point \((1,2)\) given that the slope of the tangent at any point \((x, y)\) is \(\frac{3 x}{y}\) represents

17Differential Equations

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves \(c_1 y=\left(c_2+c_3\right) e^{x+c_4}\) is

18Differential Equations

The general solution of the differential equation \(x^2 d y-2 x y d x=x^4 \cos x d x\) is

19Differential Equations

The order of the differential equation \(y=C_1 e^{C_2+x}+C_3 e^{C_4+x}\) is

20Differential Equations

The equation of the curve passing through the point \((1,1)\) such that the slope of the tangent at any point \((x, y)\) is equal to the product of its co-ordinates is

21Differential Equations

The integrating factor of the differential equation \(\left(2 x+3 y^2\right) d y=y d x(y>0)\) is

22Differential Equations

The solution of the differential equation $x \frac{d y}{d x}-y=3$ represents a family of

23Differential Equations

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

24Differential Equations

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

25Differential Equations

The integrating factor of the differential equation
$x \cdot \frac{d y}{d x}+2 y=x^2$ is $(x \neq 0)$

26Differential Equations

The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\frac{d^2 y}{d x^2}$ is

27Differential Equations

General solution of differential equations
$\frac{d y}{d x}+y=1(y \neq 1)$ is