Differential Equations PYQs - Last 10 Years

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All Differential Equations PYQs Last 5 Years Create chapter test

Practice 45 COMEDK 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 45 of 45 filtered questions.

1Differential Equations

The order and degree of the differential equation $\left(\frac{d y}{d x}\right)^2+\frac{d x}{d y}=x$ is:

2Differential Equations

\(\text { The particular solution of the equation } \sin \left(\frac{d y}{d x}\right)=a \text {, where } a \in \mathbb{R} \text { and } y=2 \text { when } x=0 \text { is }\)

3Differential Equations

In a bank the principal increases continuously at the rate of $4 \%$ per annum. In how many years will ₹ 1000 triple itself?

4Differential Equations

$$ \text { The solution of } \boldsymbol{d} \boldsymbol{y}=\boldsymbol{\operatorname { c o s }} \boldsymbol{x}(\mathbf{2}-\boldsymbol{y} \boldsymbol{\operatorname { c o s e c }} \boldsymbol{x}) \boldsymbol{d} \boldsymbol{x} \quad \text { wh...

5Differential Equations

Let the population of a species of birds surviving at a time ' $\boldsymbol{t}$ ' be governed by the differential equation $\frac{d p}{d t}-p=-100$. If $p(0)=50$, then $p\left(-\log _e 2\right)$ is equal to

6Differential Equations

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

7Differential Equations

The function $\boldsymbol{x}+\boldsymbol{y}=\boldsymbol{\operatorname { t a n }}^{-\mathbf{1}} \boldsymbol{y}$ is the solution of which of the following differential equations?

8Differential Equations

\(\text { The particular solution of the differential equation }(x-y)(d x+d y)=(d x-d y) \text { when } y=-1 \text { and } x=0 \text { is }\)

9Differential Equations

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

10Differential Equations

The order of the differential equation $\frac{d}{d x}\left[\left(\frac{d y}{d x}\right)^3\right]=0$ is

11Differential Equations

The solution of $(x+\log y) d y+y d x=0$ when $y(0)=1$ is

12Differential Equations

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

13Differential Equations

Solve the following differential equation $\cos ^2 x \frac{d y}{d x}+y=\tan x$, given that $y(0)=1$. Hence find $y\left(\frac{\pi}{4}\right)$

14Differential Equations

The solution of the differential equation: $x \cos y d y=\left(x e^x \log x+e^x\right) d x$ is

15Differential Equations

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

16Differential Equations

Find the function ' $f$ ' which satisfies the equation $\frac{d f}{d x}=2 f$, given that $f(0)=e^3$

17Differential Equations

Which of the following transformations reduce the differential equation $\frac{d z}{d x}+\frac{z}{x} \log z=\frac{z}{x^2}(\log z)^2$ into the form $\frac{d u}{d x}+P(x) u=Q(x)$

18Differential Equations

Integrating factor of the differential equation $\frac{d y}{d x}+y=\frac{x^3+y}{x}$ is

19Differential Equations

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

20Differential Equations

Solution of the differential equation $y \frac{d y}{d x}+x=0$ represents a family of

21Differential Equations

The particular solution of the differential equation \(\cos x \frac{d y}{d x}+y=\sin x\) at \(y(0)=1\)

22Differential Equations

The particular solution of \(\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0\), when \(x=0, y=\frac{1}{2}\) is

23Differential Equations

The sum of the order and degree of the differential equation \(\left(\frac{d^2 y}{d x^2}\right)^5+\frac{4\left(\frac{d^2 y}{d x^2}\right)^3}{\left(\frac{d^3 y}{d x^3}\right)}+\frac{d^3 y}{d x^3}=x^2-1\) is

24Differential Equations

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

25Differential Equations

The general solution of the differential equation \(x \frac{d y}{d x}=y+x \tan \left(\frac{y}{x}\right)\) is

26Differential Equations

\(\text { If } \frac{d y}{d x}=y+3>0 \text { and } y(0)=2 \text { then } y(\log 2) \text { is equal to }\)

27Differential Equations

Degree of the differential equation \(\log \left(\frac{d y}{d x}\right)^{\frac{1}{2}}=5 x+4 y\) is

28Differential Equations

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

29Differential Equations

\(\text { The general solution of } \frac{d y}{d x}=\sin ^{-1} x \text { is }\)

30Differential Equations

\(\text { Integrating factor of the differential equation } \frac{d y}{d x}+y=\frac{x^3+y}{x} \text { is }\)

31Differential Equations

The particular solution of \(e^{\frac{d y}{d x}}=2 x+1\) given that \(y=1\) when \(x=0\) is

32Differential Equations

The solution of the differential equation \(\frac{d y}{d x}+y \cos x=\frac{1}{2} \sin 2 x\)

33Differential Equations

The general solution of the differential equation \(\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y\)

34Differential Equations

The sum of the degree and order of the following differential equation \(\left[1-\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}=k x \frac{d^2 y}{d x^2}\)

35Differential Equations

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

36Differential Equations

The general solution of \(\left(\frac{d y}{d x}\right)^2=1-x^2-y^2+x^2 y^2\) is

37Differential Equations

The differential equation of all non-vertical lines in a plane is

38Differential Equations

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

39Differential Equations

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

40Differential Equations

The solution of the differential equation \({{{d^2}y} \over {d{x^2}}} = 0\) represents

41Differential Equations

The solution of the differential equation \((1 + {y^2}) + (x - {e^{{{\tan }^{ - 1}}y}}){{dy} \over {dx}} = 0\) is

42Differential Equations

The solution of the differential equation \(y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^2}} \over {{x^2}}}} \right)} \over {\phi '\left( {{{{y^2}} \over {{x^2}}}} \right)}}} \right]\) is (where, C is a consta...

43Differential Equations

The solution of the differential equation \({\sec ^2}x\tan ydx + {\sec ^2}y\tan xdy = 0\) is

44Differential Equations

The order and degree of the differential equation \({\left[ {1 + {{\left( {{{dy} \over {dx}}} \right)}^5}} \right]^{{1 \over 3}}} = {{{d^2}y} \over {d{x^2}}}\) are respectively

45Differential Equations

The differential equation of the family of
straight lines whose slope is equal to y-intercept
is