1
COMEDK 2024 Morning Shift
+1
-0

The particular solution of the differential equation $$\cos x \frac{d y}{d x}+y=\sin x$$ at $$y(0)=1$$

A
$$y(\sec x+\tan x)=\sec x+\tan x-x+1$$
B
$$y(\sec x+\tan x)=\sec x+\tan x-x$$
C
$$y(\sec x+\tan x)=\sec x+\tan x+x$$
D
$$y(\sec x+\tan x)=\sec x+\tan x-x+2$$
2
COMEDK 2023 Morning Shift
+1
-0

The differential equation of all non-vertical lines in a plane is

A
$$\frac{d^2 y}{d x^2}=0$$
B
$$\frac{d^2 x}{d y^2}=0$$
C
$$\frac{d y}{d x}=0$$
D
$$\frac{d x}{d y}=0$$
3
COMEDK 2023 Morning Shift
+1
-0

The general solution of $$\left(\frac{d y}{d x}\right)^2=1-x^2-y^2+x^2 y^2$$ is

A
$$2 \sin ^{-1} y=x \sqrt{1-x^2}+\sin ^{-1} x+C$$
B
$$\cos ^{-1} y=x \cos ^{-1} x$$
C
$$\sin ^{-1} y=\frac{1}{2} \sin ^{-1} x+C$$
D
$$2 \sin ^{-1} y=x \sqrt{1-y^2}+C$$
4
COMEDK 2023 Morning Shift
+1
-0

The solution of the differential equation $$\left(\frac{d y}{d x}\right) \tan y=\sin (x+y)+\sin (x-y)$$ is

A
$$\sec x=-2 \sec y+C$$
B
$$\sec y=2 \cos y+C$$
C
$$\sec y=-2 \cos x+C$$
D
$$\sec x=-2 \cos y+C$$
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