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1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The general solution of the differential equation $(x-y) d y=(x+y) d x$ is
A
$\tan ^{-1}\left(\frac{y}{x}\right)=c \sqrt{x^2+y^2}$
B
$\tan ^{-1}\left(\frac{y}{x}\right)=x^2+y^2+c$
C
$e^{\tan ^{-1}\left(\frac{y}{x}\right)}=\frac{c \sqrt{x^2+y^2}}{x}$
D
$e^{\tan ^{-1}\left(\frac{y}{x}\right)}=c \sqrt{x^2+y^2}$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The solution of the differential equation $\frac{d y}{d x}+y \log y \cot x=0$ is
A
$\cos x \log y=c$
B
$\log y=c \sin x$
C
$\sin x \log y=c$
D
$y \sin x=c$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$ \sin \left(\frac{y}{x}\right)=\frac{C}{x} $$
B
$$ \sin \left(\frac{y}{x}\right)=C x $$
C
$$ \sin \left(\frac{x}{y}\right)=C x $$
D
$$ \sin \left(\frac{x}{y}\right)=C y $$
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The general solution of the differential equation }(1+\tan y)(d x-d y)+2 x d y=0 \text { is } $$

A
$$y(\sin x+\cos x)=\sin x+c e^x$$
B
$$y(\sin x+\cos x)=\sin x+c e^{-x}$$
C
$$x(\sin y+\cos y)=\sin y+c e^y$$
D
$$x(\sin y+\cos y)=\sin y+c e^{-y}$$
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