1
MHT CET 2021 22th September Morning Shift
+2
-0

The particular solution of the diffrential equation $$y(1+\log x)=\left(\log x^x\right) \frac{d y}{d x}$$, when $$y(e)=e^2$$ is

A
$$2 e x \log x-y=e^2$$
B
$$3 ex \log y x-y=2 e^2$$
C
$$\operatorname{ex} \log x+y=2 e^2$$
D
$$\operatorname{ex} \log x-y=0$$
2
MHT CET 2021 22th September Morning Shift
+2
-0

The general solution of $$\sin ^{-1}\left(\frac{d y}{d x}\right)=x+y$$ is

A
$$\tan (x+y)-\sec (x+y)=x^2+c$$
B
$$\tan (x+y)+\sec (x+y)=x^2+c$$
C
$$\tan (x+y)+\sec (x+y)=x+c$$
D
$$\tan (x+y)-\sec (x+y)=x+c$$
3
MHT CET 2021 22th September Morning Shift
+2
-0

Solution of the differential equation $$\mathrm{y'=\frac{(x^2+y^2)}{xy}}$$, where y(1) = $$-$$2 is given by

A
$$y^2=4 x^2 \log x^2+x^2$$
B
$$y^2=x^2 \log x-x^2$$
C
$$y^2=x \log x^2+4 x^2$$
D
$$\mathrm{y}^2=\mathrm{x}^2 \log \mathrm{x}^2+4 \mathrm{x}^2$$
4
MHT CET 2021 22th September Morning Shift
+2
-0

The differential equation of all family of lines $$y=m x+\frac{4}{m}$$ obtained by eliminating the arbitrary constant $$\mathrm{m}$$ is

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