I'd love your help with finding the function $y$ from the following differential equation:
y'=\sqrt{5x+2y-3}.
I tried to use $z=5x+2-3$, so z'=5+2y' , and y'=\frac{z'}{2}-2.5
and from the equation \frac{z'}{2}-2.5=y'=\sqrt z, and then z'=2 \sqrt z+5, so $\frac{dz}{2 \sqrt z +5} = dx$, but using integration here is difficult and won't lead me to $y$.
I tries to use substitution in other ways like $z=\sqrt{5x+2y-3}$, or $z^2= 5x+2y-3$ but then again I got stuck in the middle.. Any suggestion?
Thanks a lot