Question

Solve the differential equation `y dy/dx-y^2+9x=0` ?

Answer 1

`y = sqrt( C_0 e^(2x)+9(x+1/2))`

Explanation:

Think that

`y(dy)/(dx) = 1/2 d/(dx) y^2` so the equation can be read as

`1/2 d/(dx) y^2-y^2+9x=0` now calling `z=y^2` we have

`1/2 (dz)/(dx)-z+9x=0`. This equation is easy to solve giving

`z = C_0 e^(2x)+9(x+1/2)` and finally

`y = sqrt z = sqrt( C_0 e^(2x)+9(x+1/2))`