Differential Equations PYQs - Last 10 Years
TS EAMCET / Mathematics / Calculus / 77 recent questions
MathematicsCalculus2016-2025
Practice 77 TS EAMCET 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 27 of 77 filtered questions.
1Differential Equations
The degree of the differential equation
\(x\left(\frac{d^2 y}{d x^2}\right)^{1 / 3}+2 x^2\left(\frac{d^2 y}{d x^2}\right)^{5 / 3}+7 \frac{d y}{d x}+y=0\)
\(x\left(\frac{d^2 y}{d x^2}\right)^{1 / 3}+2 x^2\left(\frac{d^2 y}{d x^2}\right)^{5 / 3}+7 \frac{d y}{d x}+y=0\)
MCQ+1 / -02022
2Differential Equations
The curve that satisfies the differential equation $x y d y-\left(1+y^2\right) d x=0$ passes through $(1,0)$ and intersects the curve $x^2+3 y^2=3$ at an angle $\theta$. Then, $\frac{2 \theta}{\pi}=$
MCQ+1 / -02022
3Differential Equations
For the differential equation
\(\sqrt{\frac{d^2 y}{d x^2}}=\sqrt[3]{\left[y \frac{d y}{d x}+x \sin \left(\frac{d y}{d x}\right)\right]^2}\)
\(\sqrt{\frac{d^2 y}{d x^2}}=\sqrt[3]{\left[y \frac{d y}{d x}+x \sin \left(\frac{d y}{d x}\right)\right]^2}\)
MCQ+1 / -02022
4Differential Equations
The differential equation corresponding to the family of curves given by $a x^2+b y^2=1$, where $a$ and $b$ are arbitrary constants is
MCQ+1 / -02022
5Differential Equations
The general solution of the differential equation $\frac{d y}{d x}=\frac{x y+x-2 y-2}{x y-2 x+y-2}$ is
MCQ+1 / -02022
6Differential Equations
The solution of the differential equation $x \cos x \frac{d y}{d x}+(x \sin x+\cos x) y=1$ is
MCQ+1 / -02020
7Differential Equations
Consider the differential equation $\frac{d y}{d x}=\frac{1}{a x+4 y+7}$ and the following statements
A. The given differential equation is linear in $x$.
B. The given differential equation is not linear in $y$.
C. The given differential eq...
A. The given differential equation is linear in $x$.
B. The given differential equation is not linear in $y$.
C. The given differential eq...
MCQ+1 / -02020
8Differential Equations
If the order and degree of the differential equation corresponding to the family of curves $(x-2)^2+(y-a)^2=b^2$, (where $a$ and $b$ are parameters) are $m$ and $n$ respectively, then $m^2+n=$
MCQ+1 / -02020
9Differential Equations
The general solution of $\frac{d y}{d x}=\frac{x+y+1}{y-x+1}$ is
MCQ+1 / -02020
10Differential Equations
The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x-3 y+4}{3 x+2 y-7}$ is
MCQ+1 / -02020
11Differential Equations
The order and degree of the differential equation $\frac{d^2 y}{d x^2}+y+\left(\frac{d y}{d x}-\frac{d^3 y}{d x^3}\right)^{3 / 2}=0$, are respectively.
MCQ+1 / -02020
12Differential Equations
The general solution of the differential equation $\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y$ is
MCQ+1 / -02020
13Differential Equations
The general solution of the differential equation $(x-2 y+1) d y-(3 x-6 y+2) d x=0$ is
MCQ+1 / -02020
14Differential Equations
The differential equation for which $l x^2+m y^2=x+y$ is the general solution is
MCQ+1 / -02020
15Differential Equations
If the solution $y(x)$ of the differential equation $\sin x \frac{d y}{d x}+y \cos x=e^{2 x}, x \in(0, \pi)$ satisfies $y\left(\frac{\pi}{2}\right)=0$, then $y\left(\frac{\pi}{6}\right)=$
MCQ+1 / -02020
16Differential Equations
The solution of the differential equation $x d y-y d x=\sqrt{x^2+y^2} d x$, given that $y=1$ when $x=\sqrt{3}$, is
MCQ+1 / -02020
17Differential Equations
If $\alpha$ and $\beta$ are respectively the order and degree of the differential equation for which $a x^2+b y^2=1$ is the general solution, then the eccentricity of the ellipse $\alpha x^2+\beta y^2=1$ is
MCQ+1 / -02020
18Differential Equations
If the general solution of the differential equation $(y-x+1) d y-(y+x+2) d x=0$ is $f(x, y, c)=0$, then the value of $c$ such that $f(1,1, c)=0$ is
MCQ+1 / -02020
19Differential Equations
If the length of the sub tangent at any point $p(x, y)$ on a curve $f(x, y)=0$ is $x+7 y^2$, then $f(x, y)=$
MCQ+1 / -02020
20Differential Equations
If the family of curves $y=a e^{4 x}+b e^{-x}$, where $a, b$ are arbitrary constants represents the general solution of the differential equation
$$ f\left(x, y \frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)=0, \text { then } \frac{d f}{d x}= ...
$$ f\left(x, y \frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)=0, \text { then } \frac{d f}{d x}= ...
MCQ+1 / -02020
21Differential Equations
Let $f:[2,5] \rightarrow \mathbf{R}$ be a differentiatiable function and $\frac{f(5)}{f(2)}=1$. If there is a $c \in(2,5)$ such that $c f^{\prime}(c)=2 f(c)-2 c^3$, then $f(x)=$
MCQ+1 / -02020
22Differential Equations
Let $f:[2,5] \rightarrow \mathbf{R}$ be a differentiatiable function and $\frac{f(5)}{f(2)}=1$. If there is a $c \in(2,5)$ such that $c f^{\prime}(c)=2 f(c)-2 c^3$, then $f(x)=$
MCQ+1 / -02020
23Differential Equations
The general solution of the differential equation $x \cos \frac{y}{x}(y d x+x d y)=y \sin \frac{y}{x}(x d y-y d x)$ is
MCQ+1 / -02020
24Differential Equations
The general solution of the differential equation $(3 y-7 x+7) d x+(7 y-3 x+3) d y=0$ is
MCQ+1 / -02020
25Differential Equations
If $y=e^{a x}(\cos b x+\sin b x)$ satisfies the equation $\frac{d^2 y}{d x^2}-K \frac{d y}{d x}+L y=0$, then $L+b K=$
MCQ+1 / -02020
26Differential Equations
The general solution of the differential equation
$(3 y-7 x+7) d x+(7 y-3 x+3) d y=0$ is
$(3 y-7 x+7) d x+(7 y-3 x+3) d y=0$ is
MCQ+1 / -02020
27Differential Equations
The differential equation for which $y=a x^2+b x+c$ is the general solution is
MCQ+1 / -02020