# How do you find the solution to the differential equation dy/dx=cos(x)/y^2 where y(π/2)=0?

Mar 8, 2015

You can write:
${y}^{2} \mathrm{dy} = \cos \left(x\right) \mathrm{dx}$
and integrate;
$\int {y}^{2} \mathrm{dy} = \int \cos \left(x\right) \mathrm{dx}$
Which gives you:
${y}^{3} / 3 = \sin \left(x\right) + c$
${y}^{3} = 3 \sin \left(x\right) + c$
Now we find the value of $c$;
${\left(0\right)}^{3} = 3 \sin \left(\frac{\pi}{2}\right) + c$
$0 = 3 + c$
And $c = - 3$
${y}^{3} = 3 \sin \left(x\right) - 3$