ODE
\[ a (a+2)^2 y(x) y''(x)=a^2 (a+2) y(x)^3 f'(x)-a^2 f(x)^2 y(x)^4+a (a+2)^2 f(x) y(x)^2 y'(x)+(a-1) (a+2)^2 y'(x)^2 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 0.960022 (sec), leaf count = 0 , could not solve
DSolve[a*(2 + a)^2*y[x]*Derivative[2][y][x] == -(a^2*f[x]^2*y[x]^4) + a^2*(2 + a)*y[x]^3*Derivative[1][f][x] + a*(2 + a)^2*f[x]*y[x]^2*Derivative[1][y][x] + (-1 + a)*(2 + a)^2*Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 2.858 (sec), leaf count = 0 , could not solve
dsolve(a*(a+2)^2*y(x)*diff(diff(y(x),x),x) = (a-1)*(a+2)^2*diff(y(x),x)^2+a*(a+2)^2*f(x)*y(x)^2*diff(y(x),x)+a^2*(a+2)*diff(f(x),x)*y(x)^3-a^2*f(x)^2*y(x)^4, y(x),'implicit')
Mathematica raw input
DSolve[a*(2 + a)^2*y[x]*y''[x] == -(a^2*f[x]^2*y[x]^4) + a^2*(2 + a)*y[x]^3*f'[x] + a*(2 + a)^2*f[x]*y[x]^2*y'[x] + (-1 + a)*(2 + a)^2*y'[x]^2,y[x],x]
Mathematica raw output
DSolve[a*(2 + a)^2*y[x]*Derivative[2][y][x] == -(a^2*f[x]^2*y[x]^4) + a^2*(2 + a)*y[x]^3*Derivative[1][f][x] + a*(2 + a)^2*f[x]*y[x]^2*Derivative[1][y][x] + (-1 + a)*(2 + a)^2*Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(a*(a+2)^2*y(x)*diff(diff(y(x),x),x) = (a-1)*(a+2)^2*diff(y(x),x)^2+a*(a+2)^2*f(x)*y(x)^2*diff(y(x),x)+a^2*(a+2)*diff(f(x),x)*y(x)^3-a^2*f(x)^2*y(x)^4, y(x),'implicit')
Maple raw output
dsolve(a*(a+2)^2*y(x)*diff(diff(y(x),x),x) = (a-1)*(a+2)^2*diff(y(x),x)^2+a*(a+2)^2*f(x)*y(x)^2*diff(y(x),x)+a^2*(a+2)*diff(f(x),x)*y(x)^3-a^2*f(x)^2*y(x)^4, y(x),'implicit')