Question

general solution to u'=u^1/2 when u(0)=1

Answer 1

So you know to integrate both sides?

Answer 2

yeah you get 2u^1/2=t+C right?

Answer 3

\[\frac{du}{dt}=u^\frac{1}{2}\]
\[\frac{du}{u^\frac{1}{2}}=1 dt\]

Answer 4

this is a differential equation problem with separation of variables

Answer 5

now you integrate both sides lol

Answer 6

\[\frac{du}{dt}=\sqrt{u}\]
\[\frac{du}{\sqrt{u}}=dt\]
\[\int_{}{}\frac{du}{\sqrt{u}}=\int_{}{}dt\]

Answer 7

So yes what you have is right :) so far

Answer 8

\[\frac{1}{\sqrt{u}}=u^{-1/2}\]

Answer 9

Now apply you initial condition

Answer 10

so C=2u^1/2 - 1?

Answer 11

u(0)=1
Means we want to find C when t=0 and u=1

Answer 12

oh ok so C=2

Answer 13

Yep :)

Answer 14

thanks then there was one i didnt understand
u'=u/4+u^2 do you multiply by the reciprocal to both sides so all your u's are on one side?

Answer 15

giving you integral of (4+u^2/u)=t+C