Embibe Experts Solutions for Exercise 6: Assignment

If a mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the diameter of the ball decreases from $2 \mathrm{cm}$ to $1 \mathrm{cm}$ in$3$ months, so the time before which the ball has practically gone is

Let $x(1-x)\frac{dy}{dx}=x-y$ then

Let a curve passes through$(3,2)$ and satisfied the differential equation$(x-1) d x+4(y-2) d y=0$

A curve satisfies the differential equation $\frac{dy}{dx}=\frac{x+1-x{y}^2}{x^{2}y-y}$ and passes through$(0,0)$

$y=c_{1}x+c_2\sin \left(2x+c_3\right), (c_1,c_2,c_3$are arbitrary constants)

Which of the following statements is/are true?

A curve passes through$(1,0)$ and satisfies the defferential equation $\left(2x\cos y+3x^{2}y\right) dx+$

$\left(x^3-x^2\sin y-y\right)dy=0$

Let $y^{\text{'}}\left(x\right)+y\left(x\right)g^{\text{'}}\left(x\right)=g\left(x\right)g^{\text{'}}\left(x\right), y\left(0\right)=0, x\in R$, where $f^{\text{'}}\left(x\right)$ denotes $\frac{df\left(x\right)}{dx}$and $g\left(x\right)$ is a given non-constant differentiable function on $R$ with $g\left(0\right)=g\left(2\right)=0$. Then the value of $y\left(2\right)$ is