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
odeadvisor timed out
Book solution method
TO DO
Mathematica ✓
cpu = 21.4887 (sec), leaf count = 41
\[\left \{\left \{y(x)\to -\frac {(a+2) (x+c_1){}^a}{a \int _1^xf(K[3]) (c_1+K[3]){}^adK[3]+c_2}\right \}\right \}\]
Maple ✗
cpu = 3.503 (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))
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
{{y[x] -> -(((2 + a)*(x + C[1])^a)/(C[2] + a*Inactive[Integrate][f[K[3]]*(C[1] + K[3])^a, {K[3], 1, 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))
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))