Separable differential equationsAQA A-Level Maths: Mind map

Exam questions on Separable differential equations

1. A curve satisfies the differential equation $\frac{dy}{dx}=2xy$, where $y>0$.
   Given that $y=3$ when $x=0$, find $y$ in terms of $x$.2 marks
2. A particle moves in a straight line. Its velocity $v$ m s$^{-1}$ at time $t$ seconds satisfies $\frac{dv}{dt}=-0.5v$, and $v=8$ when $t=0$.
   Explain, using your solution, why the model predicts that the particle never comes to rest, and suggest why this is unrealistic.2 marks
3. A curve satisfies the differential equation $\frac{dy}{dx}=6x+3xy$ for $x\ge0$.
   Show that the general solution can be written $y=Ae^{\frac32x^2}-2$, where $A$ is a constant.3 marks