Find a general solution to the first – degree ODE. If an initial condition is given, find the corresponding particular solution. Write solution explicitly if possible.
(9x^2+y-1)dx-(4y-x)dy=0, y(1)=0
This is an exact equation. If
P(x,y) = 9x^2+y-1
Q(x,y) = x-4y
∂P/∂y = ∂Q/∂x
So, we have
3x^3 - x - 2y^2 + xy = c
Since y(1) = 0,
3 - 1 - 0 + 0 = c so c=2