Question

dy/dx= (5x^2)/sqrt(y)
and y=1 when x=0
Use separation of variables to solve the initial value problem

Answer 1

\[\Large\bf\sf \frac{dy}{dx}=\frac{5x^2}{\sqrt y},\qquad y(0)=1\]Ok what are you stuck on? :O

Answer 2

ok when i do it i got y=((5x^3)/2)^3/2

Answer 3

is that correct?

Answer 4

Hmm let's check.

Answer 5

\[\Large\bf\sf \int\limits \sqrt y \;dy\quad=\quad \int\limits 5x^2\;dx\]Gives us,\[\Large\bf\sf \frac{2}{3}y^{3/2}\quad=\quad \frac{5}{3}x^3+C\]

Answer 6

Multiply both sides by 2/3,\[\Large\bf\sf y^{3/2}\quad=\quad \frac{5}{2}x^3+c\]

Answer 7

Plug in our initial data,\[\Large\bf\sf 1\quad=\quad \frac{5}{2}\cdot 0+c\qquad\implies\qquad c=1\]

Answer 8

Did you get your c value messed up maybe? Hmm

Answer 9

i think that might be

Answer 10

is it