1
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.
2
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.
3
MHT CET 2023 11th May Morning Shift
+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.
4
MHT CET 2023 11th May Morning Shift
+2
-0

A curve passes through the point $$\left(1, \frac{\pi}{6}\right)$$. Let the slope of the curve at each point $$(x, y)$$ be $$\frac{y}{x}+\sec \left(\frac{y}{x}\right), x>0$$, then, the equation of the curve is

A
$$\sin \left(\frac{y}{x}\right)=\log (x)+\frac{1}{2}$$
B
$$\operatorname{cosec}\left(\frac{y}{x}\right)=\log (x)+2$$
C
$$\sec \left(\frac{2 y}{x}\right)=\log (x)+2$$
D
$$\cos \left(\frac{2 y}{x}\right)=\log (x)+\frac{1}{2}$$
EXAM MAP
Medical
NEET