Question

if dy/dx=(1/4)y and y(0)=5 then y(4)=

Answer 1

you can use separation of variables to solve y'=y/4

Answer 2

So dy/y=dx/4
Integrate both sides:
Ln|y|=x/4+c

Answer 3

But y(0)=5 then c=ln5

Answer 4

So ln|y|=1+ln5 when replace x=4
--> y=e^(1+ln5)
I hope this is helpful :)