ODE
\[ g(x) (f(x)-y(x)) \sqrt {(y(x)-a) (y(x)-b)}+y'(x)=0 \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Change of Variable, new dependent variable
Mathematica ✗
cpu = 2.98454 (sec), leaf count = 0 , could not solve
DSolve[g[x]*(f[x] - y[x])*Sqrt[(-a + y[x])*(-b + y[x])] + Derivative[1][y][x] == 0, y[x], x]
Maple ✗
cpu = 0.755 (sec), leaf count = 0 , could not solve
dsolve(diff(y(x),x)+(f(x)-y(x))*g(x)*((y(x)-a)*(y(x)-b))^(1/2) = 0, y(x),'implicit')
Mathematica raw input
DSolve[g[x]*(f[x] - y[x])*Sqrt[(-a + y[x])*(-b + y[x])] + y'[x] == 0,y[x],x]
Mathematica raw output
DSolve[g[x]*(f[x] - y[x])*Sqrt[(-a + y[x])*(-b + y[x])] + Derivative[1][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(y(x),x)+(f(x)-y(x))*g(x)*((y(x)-a)*(y(x)-b))^(1/2) = 0, y(x),'implicit')
Maple raw output
dsolve(diff(y(x),x)+(f(x)-y(x))*g(x)*((y(x)-a)*(y(x)-b))^(1/2) = 0, y(x),'implicit')