\[ -y(x) f''(x)+f'(x) y'(x)+f(x) y(x)^3+y(x) y''(x)-y'(x)^2-y(x)^4=0 \] ✓ Mathematica : cpu = 0.510345 (sec), leaf count = 308
\[\left \{\left \{y(x)\to -\frac {\exp \left (c_2-\int _1^x\frac {y(K[3])^4-f(K[3]) y(K[3])^3+c_1{}^2 y(K[3])^2+\int _1^{K[3]}\frac {-y(K[1])^4+f(K[1]) y(K[1])^3-f''(K[1]) y(K[1])+f'(K[1]) y'(K[1])}{y(K[1])^2}dK[1]{}^2 y(K[3])^2+2 c_1 \int _1^{K[3]}\frac {-y(K[1])^4+f(K[1]) y(K[1])^3-f''(K[1]) y(K[1])+f'(K[1]) y'(K[1])}{y(K[1])^2}dK[1] y(K[3])^2+f''(K[3]) y(K[3])-f'(K[3]) y'(K[3])}{y(K[3])^2 \left (c_1+\int _1^{K[3]}\frac {-y(K[1])^4+f(K[1]) y(K[1])^3-f''(K[1]) y(K[1])+f'(K[1]) y'(K[1])}{y(K[1])^2}dK[1]\right )}dK[3]\right )}{\int _1^x\frac {-y(K[1])^4+f(K[1]) y(K[1])^3-f''(K[1]) y(K[1])+f'(K[1]) y'(K[1])}{y(K[1])^2}dK[1]+c_1}\right \}\right \}\] ✗ Maple : cpu = 0. (sec), leaf count = 0
, could not solve
dsolve(diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+diff(f(x),x)*diff(y(x),x)-diff(diff(f(x),x),x)*y(x)+f(x)*y(x)^3-y(x)^4=0,y(x))