Solving ODE by separation of variables

Calculus Level 1

Find the solution of the following ordinary differential equation: d r d t = 2 t r , r ( 0 ) = r 0 . \frac { dr }{ dt }=-2tr, \quad r(0)={r}_{0} .

r = r 0 e r 0 t 2 r={r}_{0}{e}^{-{r}_{0}{t}^{2}} r = r 0 e t 2 r={r}_{0}{e}^{-{t}^{2}} r = r 0 e r 0 2 t 2 r={r}_{0}{e}^{-{{r}_{0}}^{2}{t}^{2}} r = r 0 e t r={r}_{0}{e}^{-{t}}

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Md Zuhair
Aug 5, 2016

d r / r = 2 t d t dr/r = -2t dt ... Integrate both sides l o g r = t 2 logr= -t^2 and r = e ( t ) 2 r= e^(-t)^2

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...