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1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The solution of $(x+\log y) d y+y d x=0$ when $y(0)=1$ is
A
$y(x-1+\log y)+1=0$
B
$x y+y \log y+1=0$
C
$x y=y \log y-y-1$
D
$y(x+1+\log y)-1=0$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The order of the differential equation $\frac{d}{d x}\left[\left(\frac{d y}{d x}\right)^3\right]=0$ is
A
not defined
B
1
C
2
D
3
3
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
$e^{\tan ^{-1}\left(\frac{y}{x}\right)}=c \sqrt{x^2+y^2}$
4
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
$y \sin x=c$
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