1
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$ y e^{\sin x}=e^{\sin x}(\sin x+1)+c $$
B
$$ y e^{\sin x}=e^{\sin x}(\sin x-1)+c $$
C
$$ y e^{\sin 2 x}=e^{\sin 2 x}(\sin x-1)+c $$
D
$$ y e^{\cos x}=e^{\sin x}(\cos x-1)+c $$
2
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$\frac{5}{2}$$
B
4
C
$$\frac{3}{2}$$
D
3
3
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

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

A
all circles in a plane
B
all straight lines in a plane
C
all parabolas in a plane
D
all ellipses in a plane
4
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

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

A
$$\cos ^{-1} x+\cos ^{-1} y=c$$
B
$$\sin ^{-1} x+\sin ^{-1} y=c$$
C
$$\cosh ^{-1} x+\cosh ^{-1} y=c$$
D
$$\sinh ^{-1} x+\sinh ^{-1} y=c$$
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