1
MHT CET 2023 9th May Evening Shift
+2
-0

General solution of the differential equation $$\log \left(\frac{d y}{d x}\right)=a x+b y$$ is

A
$$a e^{b y}+b e^{a x}=c_1$$, where $$c_1$$ is a constant.
B
$$a e^{-b y}+b^{-a x}=c_1$$, where $$c_1$$ is a constant.
C
$$a e^{-b y}+b e^{a x}=c_1$$, where $$c_1$$ is a constant.
D
$$a e^{b y}+b e^{-a x}=c_1$$, where $$c_1$$ is a constant.
2
MHT CET 2023 9th May Evening Shift
+2
-0

The differential equation of all circles which pass through the origin and whose centres lie on $$\mathrm{Y}$$-axis is

A
$$\left(x^2-y^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}-2 x y=0$$
B
$$\left(x^2-y^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+2 x y=0$$
C
$$\left(x^2-y^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+x y=0$$
D
$$\left(x^2-y^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}-x y=0$$
3
MHT CET 2023 9th May Morning Shift
+2
-0

The differential equation of all parabolas, whose axes are parallel to $$\mathrm{Y}$$-axis, is

A
$$y_3=1$$
B
$$y_3=0$$
C
$$y_3=-1$$
D
$$y y_3+y_1=0$$
4
MHT CET 2023 9th May Morning Shift
+2
-0

The particular solution of the differential equation $$\left(1+y^2\right) \mathrm{d} x-x y \mathrm{~d} y=0$$ at $$x=1, y=0$$, represents

A
circle
B
pair of straight lines
C
hyperbola
D
ellipse
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