ODE
\[ y(x) y''(x)=y(x)^2 \left (f(x) y(x)+g'(x)\right )+y'(x)^2+y'(x) \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 5.63177 (sec), leaf count = 0 , could not solve
DSolve[y[x]*Derivative[2][y][x] == y[x]^2*(f[x]*y[x] + Derivative[1][g][x]) + Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 0.423 (sec), leaf count = 0 , could not solve
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+diff(y(x),x)+y(x)^2*(f(x)*y(x)+diff(g(x),x)), y(x),'implicit')
Mathematica raw input
DSolve[y[x]*y''[x] == y[x]^2*(f[x]*y[x] + g'[x]) + y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
DSolve[y[x]*Derivative[2][y][x] == y[x]^2*(f[x]*y[x] + Derivative[1][g][x]) + Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+diff(y(x),x)+y(x)^2*(f(x)*y(x)+diff(g(x),x)), y(x),'implicit')
Maple raw output
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+diff(y(x),x)+y(x)^2*(f(x)*y(x)+diff(g(x),x)), y(x),'implicit')