1
MHT CET 2023 10th May Evening Shift
+2
-0

The general solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+\left(\frac{3 x^2}{1+x^3}\right) y=\frac{1}{x^3+1}$$ is

A
$$y\left(1+x^3\right)=x^3+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$y\left(1+x^3\right)=x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$y\left(1+x^3\right)=x^2+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$y\left(1+x^3\right)=2 x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
2
MHT CET 2023 10th May Evening Shift
+2
-0

The differential equation of all circles, passing through the origin and having their centres on the $$\mathrm{X}$$-axis, is

A
$$y^2=x^2+x y \frac{\mathrm{d} y}{\mathrm{~d} x}$$
B
$$x^2=y^2+2 x y \frac{\mathrm{d} y}{\mathrm{~d} x}$$
C
$$y^2=x^2+2 x y \frac{\mathrm{d} y}{\mathrm{~d} x}$$
D
$$x^2=y^2-x y \frac{\mathrm{d} y}{\mathrm{~d} x}$$
3
MHT CET 2023 10th May Morning Shift
+2
-0

The population $$\mathrm{P}=\mathrm{P}(\mathrm{t})$$ at time $$\mathrm{t}$$ of certain species follows the differential equation $$\frac{d P}{d t}=0.5 P-450$$. If $$P(0)=850$$, then the time at which population becomes zero is

A
$$2 \log 18$$
B
$$\log 9$$
C
$$\frac{1}{2} \log 18$$
D
$$\log 18$$
4
MHT CET 2023 10th May Morning Shift
+2
-0

The differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\sqrt{1-y^2}}{y}$$ determines a family of circles with

A
variable radii and fixed centre at $$(0,1)$$.
B
variable radii and fixed centre at $$(0,-1)$$.
C
fixed radius of 1 unit and variable centre along the $$\mathrm{Y}$$-axis.
D
fixed radius of 1 unit and variable centre along the $$\mathrm{X}$$-axis.
EXAM MAP
Medical
NEET