1
MHT CET 2023 12th May Morning Shift
MCQ (Single Correct Answer)
+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
2
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+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.
3
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+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.
4
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$$x+y=\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$x-y=\mathrm{c}(x y)$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$x+y=\mathrm{c}(1+x y)$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$y-x=\mathrm{c}(1+x y)$$, where $$\mathrm{c}$$ is a constant of integration.
MHT CET Subjects
EXAM MAP