1
MHT CET 2021 24th September Morning Shift
+2
-0

The particular solution of the differential equation $$\frac{d y}{d x}=\frac{x+y+1}{x+y-1}$$ when $$\mathrm{x}=\frac{2}{3}$$ and $$y=\frac{1}{3}$$ is

A
$$2 x+2 y-2=\log |x+y|$$
B
$$y-x+\frac{1}{3}=\log |x+y|$$
C
$$x+y-1=\log |x+y|$$
D
$$4 x-5 y-1=\log |x+y|$$
2
MHT CET 2021 24th September Morning Shift
+2
-0

The order of the differential equation whose solution is $$y=a \cos x+b \sin x+c e^{-x}$$ is

A
3
B
4
C
2
D
1
3
MHT CET 2021 24th September Morning Shift
+2
-0

The general solution of the differential equation $$(2 y-1) d x-(2 x+3) d y=0$$ is

A
$$(2 x+3)^2=c(2 y-1)$$
B
$$\frac{2 x+3}{2 y-1}=c$$
C
$$(2 x+3)(2 y-1)=c$$
D
$$(2 x+3)(2 y-1)^2=c$$
4
MHT CET 2021 24th September Morning Shift
+2
-0

The differential equation of the family of parabolas with focus at the origin and the $$X$$-axis a axis, is

A
$$-y\left(\frac{d y}{d x}\right)^2=2 x \frac{d y}{d x}-y$$
B
$$y\left(\frac{d y}{d x}\right)^2+2 x y \frac{d y}{d x}+y=0$$
C
$$y\left(\frac{d y}{d x}\right)^2+4 x \frac{d y}{d x}=4 x y$$
D
$$y\left(\frac{d y}{d x}\right)^2+y=2 x y \frac{d y}{d x}$$
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