Separable differential equationsEdexcel A-Level Maths: Mind map

Exam questions on Separable differential equations

1. A curve satisfies the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x}=2xy$ with $y>0$.
   Given that $y=3$ when $x=0$, find the exact value of $y$ when $x=1$.2 marks
2. The mass $m$ grams of a radioactive sample at time $t$ years satisfies $\frac{\mathrm{d}m}{\mathrm{d}t}=-0.05m$. Initially the mass is $80$ g.
   Find the time taken for the mass to fall to $40$ g, giving your answer in years to 3 significant figures.2 marks
3. A particle moves in a straight line. Its velocity $v$ m s$^{-1}$ at time $t$ seconds satisfies $\frac{\mathrm{d}v}{\mathrm{d}t}=-0.4v^2$, and $v=5$ when $t=0$.
   Show that $v=\frac{5}{2t+1}$.3 marks