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

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

A
4
B
5
C
6
D
8
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
5
B
13
C
$$-$$2
D
7
3
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
$$ y=c e^{\left(\frac{x^2}{y^2}\right)} $$
4
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
$$ x e^x $$
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