1
MHT CET 2023 12th May Morning Shift
+2
-0

The differential equation $$\cos (x+y) \mathrm{d} y=\mathrm{d} x$$ has the general solution given by

A
$$y=\sin (x+y)+c$$, where $$\mathrm{c}$$ is a constant.
B
$$y=\tan (x+y)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant
C
$$y=\tan \left(\frac{x+y}{2}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant
D
$$y=\frac{1}{2} \tan (x+y)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant
2
MHT CET 2023 12th May Morning Shift
+2
-0

If $$\frac{\mathrm{d} y}{\mathrm{~d} x}=y+3$$ and $$y(0)=2$$, then $$y(\log 2)=$$

A
5
B
7
C
13
D
$$-$$2
3
MHT CET 2023 11th May Evening Shift
+2
-0

The solution of $$\frac{\mathrm{d} x}{\mathrm{~d} y}+\frac{x}{y}=x^2$$ is

A
$$\frac{1}{y}=\mathrm{c} x-x \log x$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\frac{1}{x}=\mathrm{c} y-y \log y$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$\frac{1}{x}=\mathrm{c} x-x \log y$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$\frac{1}{y}=\mathrm{c} x-y \log x$$, where $$\mathrm{c}$$ is a constant of integration.
4
MHT CET 2023 11th May Evening Shift
+2
-0

The solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{y}{x}=\sin x$$ is

A
$$x y+\cos x=\sin x+\mathrm{c}$$, where c is a constant of integration.
B
$$x(y+\cos x)=\sin x+\mathrm{c}$$, where c is a constant of integration.
C
$$y(x+\cos x)=\sin x+c$$, where c is a constant of integration.
D
$$x y+\sin x=\cos x+\mathrm{c}$$, where c is a constant of integration.
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