1
COMEDK 2025 Evening Shift
MCQ (Single Correct Answer)
+1
-0
Find the function ' $f$ ' which satisfies the equation $\frac{d f}{d x}=2 f$, given that $f(0)=e^3$
A
$2 x+3$
B
$\log (2 x+3)$
C
$e^{2 x+3}$
D
$\frac{x^2}{2}$
2
COMEDK 2025 Evening Shift
MCQ (Single Correct Answer)
+1
-0
Solve the following differential equation $\cos ^2 x \frac{d y}{d x}+y=\tan x$, given that $y(0)=1$. Hence find $y\left(\frac{\pi}{4}\right)$
A
2
B
$\frac{2}{e}$
C
e
D
1
3
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
Integrating factor of the differential equation $\frac{d y}{d x}+y=\frac{x^3+y}{x}$ is
A
$\frac{x}{e^x}$
B
$e^x$
C
$\frac{e^x}{x}$
D
$x e^x$
4
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{4}}=\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{3}}$
A
4
B
9
C
6
D
2
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