Consider the differential equation $\left(2 x y-y^{n}\right) d x+x^{2} d y=0$. Which of the following statements is NOT TRUE? (A) For $n=1$ the differential equation is v...

Consider the differential equation $\frac{d x}{d y}=\frac{y^{2}+y^{2} e^{\left(\frac{x}{y}\right)^{2}}+2 x^{2} e^{\left(\frac{x}{y}\right)^{2}}}{2 x y e^{\left(\frac{x}{y...

Which of the following equations are separable?a. $\dot{y}=\sin (t y)$b. $\dot{y}=e^{t} e^{y}$c. $y \dot{y}=t$d. $\dot{y}=\left(t^{3}-t\right) \arcsin (y)$e. $\dot{y}=t^{...

Separable equations. Solve the following initial value problems.(a) $y^{\prime}=x^{3}(1-y), \quad y(0)=3$;(b) $d y / d \theta=y \sin \theta, \quad y(0)=\sqrt{3}$;(c) $d y...