1
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
Which of the following transformations reduce the differential equation $\frac{d z}{d x}+\frac{z}{x} \log z=\frac{z}{x^2}(\log z)^2$ into the form $\frac{d u}{d x}+P(x) u=Q(x)$
A
$u=(\log z)^{-1}$
B
$u=\log x$
C
$u=(\log z)^2$
D
$u=e^x$
2
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
Solution of the differential equation $y \frac{d y}{d x}+x=0$ represents a family of
A
Ellipse
B
Parabola
C
Circles
D
Hyperbola
3
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
$y(x+1+\log y)-1=0$
4
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
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