ODE
\[ y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-u(x))^2 \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Change of variable
Mathematica ✗
cpu = 1.90824 (sec), leaf count = 0 , could not solve
DSolve[Derivative[1][y][x]^2 == f[x]^2*(-a + y[x])*(-b + y[x])*(-u[x] + y[x])^2, y[x], x]
Maple ✗
cpu = 496.507 (sec), leaf count = 0 , could not solve
dsolve(diff(y(x),x)^2 = f(x)^2*(y(x)-u(x))^2*(y(x)-a)*(y(x)-b), y(x),'implicit')
Mathematica raw input
DSolve[y'[x]^2 == f[x]^2*(-a + y[x])*(-b + y[x])*(-u[x] + y[x])^2,y[x],x]
Mathematica raw output
DSolve[Derivative[1][y][x]^2 == f[x]^2*(-a + y[x])*(-b + y[x])*(-u[x] + y[x])^2, y[x], x]
Maple raw input
dsolve(diff(y(x),x)^2 = f(x)^2*(y(x)-u(x))^2*(y(x)-a)*(y(x)-b), y(x),'implicit')
Maple raw output
dsolve(diff(y(x),x)^2 = f(x)^2*(y(x)-u(x))^2*(y(x)-a)*(y(x)-b), y(x),'implicit')