1
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$ y=c e^{\left(\frac{x^2}{2 y^2}\right)} $$
B
$$ y=c e^{\left(\frac{x^2}{3 y^2}\right)} $$
C
$$ y=c e^{\left(-\frac{x^2}{2 y^2}\right)} $$
D
$$ y=c e^{\left(\frac{x^2}{y^2}\right)} $$
2
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$ \frac{x}{e^x} $$
B
$$ e^x $$
C
$$ \frac{e^x}{x} $$
D
$$ x e^x $$
3
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$ y=x \sin ^{-1} x+\sqrt{1-x^2}+C $$
B
$$ y=x \sin ^{-1} x-\sqrt{1-x^2}+C $$
C
$$ y=-x \sin ^{-1} x+\sqrt{1-x^2}+C $$
D
$$ y=-x \sin ^{-1} x-\sqrt{1-x^2}+C $$
4
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

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

A
Not defined
B
4
C
1
D
2
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