Question

Resolva a equação diferencial linear tdy/dt + 2y= t^3

Answer 1

$ty'+2y=t^3\\ \\ (yt)'+y=t^3\\ \\ \text{Seja }z=yt\\ \\ z'+\dfrac{z}{t}=t^3\\ \\ tz'+z=t^4\\ \\ (zt)'=t^4\\ \\ \displaystyle zt=\int t^4~dt\\ \\ \\ zt=\dfrac{t^5}{5}+C\\ \\ \\ yt^2=\dfrac{t^5}{5}+C\\ \\ \\ \boxed{y(t)=\dfrac{t^3}{5}+\dfrac{C}{t^2}}$