- #1

karush

Gold Member

MHB

- 3,269

- 5

$y'=-1-2y$

$\begin{array}{ll}

rewrite &y'+2y=-1\\

exp &u(t)=\exp\ds\int 2 \, dx=e^{2t}\\

product &(e^{2t}y)'=-e^{2t}\\

&e^{2t}y=\ds\int -e^{2t} \, dt=\dfrac{-e^(2 t)}{2}+c\\

hence &y(t)=\dfrac{-e^{2t}}{2} + \dfrac{c}{e^{2t}}\\

t \to \infty &=-\dfrac{1}{2}+0\\

so &y \to \dfrac{1}{2}\textit{ as t} \to \infty

\end{array}$

ok this is an early problem but probably some comments to make it more understandable

hopefully correct

I was going to try tikz on this but probably 3 pages of code so its a desmos templatehttps://dl.orangedox.com/geAQogxCM0ZYQLaUju