1
MHT CET 2021 23th September Morning Shift
+2
-0

The general solution of the differential equation $$\frac{d y}{d x}+\frac{y^2+y+1}{x^2+x+1}=0$$ is

A
$$x+y+1=c(1+x+y+2 x y)$$
B
$$x+y+1=c(2+x+y+2 x y)$$
C
$$x+y+1=c(1-x-y-2 x y)$$
D
$$x+y+2=c(2-x-y-2 x y)$$
2
MHT CET 2021 23th September Morning Shift
+2
-0

The general solution of the differential equation $$\frac{d x}{d t}=\frac{x \log x}{t}$$ is

A
$$\log x-x=c$$
B
$$e^{c t}+x=0$$
C
$$\log t=x+c$$
D
$$e^{c t}=x$$
3
MHT CET 2021 23th September Morning Shift
+2
-0

The particular solution of differential equation $$(x+y) d y+(x-y) d x=0$$ at $$x=y=1$$ is

A
$$\log \left|\frac{x^2+y^2}{2}\right|=\frac{\pi}{2}-2 \tan ^{-1}\left(\frac{y}{x}\right)$$
B
$$\log \left|x^2+y^2\right|=\frac{\pi}{2}-2 \tan ^{-1}\left(\frac{y}{x}\right)$$
C
$$\log \left|x^2+y^2\right|=\frac{\pi}{2}-2 \tan ^{-1}\left(\frac{y}{x}\right)$$
D
$$\log \left|\frac{x^2+y^2}{2}\right|=\frac{\pi}{4}-2 \tan ^{-1}\left(\frac{y}{x}\right)$$
4
MHT CET 2021 23th September Morning Shift
+2
-0

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

A
$$2^x-2^y=c$$
B
$$\frac{1}{2^x}-\frac{1}{2^y}=c$$
C
$$\frac{1}{2^x}+\frac{1}{2^y}=c$$
D
$$2^x+2^y=c$$
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