1
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $$\left(3 x y+y^2\right) d x+\left(x^2+x y\right) d y=0$$ is

A
$$x^2\left(2 x y-y^2\right)=c$$
B
$$x^2\left(y^2-2 x y\right)=c$$
C
$$x\left(2 x y+y^2\right)=c$$
D
$$x^2\left(2 x y+y^2\right)=c$$
2
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The differential equation of family of circles whose centres lie on $$\mathrm{X}$$-axis is

A
$$\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2+1=0$$
B
$$y\left(\frac{d^2 y}{d x^2}\right)+\left(\frac{d y}{d x}\right)^2+1=0$$
C
$$y\left(\frac{d^2 y}{d x^2}\right)-\left(\frac{d y}{d x}\right)^2-1=0$$
D
$$y\left(\frac{d^2 y}{d x^2}\right)+\left(\frac{d y}{d x}\right)^2-1=0$$
3
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $$y(1+\log x)\left(\frac{d x}{d y}\right)-x \log x=0$$ is

A
$$y(1+\log x)=c$$
B
$$x \log x=y c$$
C
$$x \log x=y+c$$
D
$$\log x-y=c$$
4
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $$\frac{d y}{d x}=\frac{x+2 y-1}{x+2 y+1}$$ is

A
$$3(x+y)+4 \log |3 x+6 y-1|=K$$
B
$$3(x-y)+4 \log |3 x+6 y-1|=K$$
C
$$6(-x+y)+4 \log |3 x+6 y-1|=K$$
D
$$6(x+y)+4 \log |3 x+6 y-1|=K$$
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