ODE
\[ y''(x)=y'(x) (\text {f0}(x) y(x)+\text {f1}(x))+\text {g0}(x) y(x)^3+\text {g1}(x) y(x)^2+\text {g2}(x) y(x)+\text {g3}(x) \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 0.60001 (sec), leaf count = 0 , could not solve
DSolve[Derivative[2][y][x] == g3[x] + g2[x]*y[x] + g1[x]*y[x]^2 + g0[x]*y[x]^3 + (f1[x] + f0[x]*y[x])*Derivative[1][y][x], y[x], x]
Maple ✗
cpu = 1.124 (sec), leaf count = 0 , could not solve
dsolve(diff(diff(y(x),x),x) = (f0(x)*y(x)+f1(x))*diff(y(x),x)+g0(x)*y(x)^3+g1(x)*y(x)^2+g2(x)*y(x)+g3(x), y(x),'implicit')
Mathematica raw input
DSolve[y''[x] == g3[x] + g2[x]*y[x] + g1[x]*y[x]^2 + g0[x]*y[x]^3 + (f1[x] + f0[x]*y[x])*y'[x],y[x],x]
Mathematica raw output
DSolve[Derivative[2][y][x] == g3[x] + g2[x]*y[x] + g1[x]*y[x]^2 + g0[x]*y[x]^3 + (f1[x] + f0[x]*y[x])*Derivative[1][y][x], y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x) = (f0(x)*y(x)+f1(x))*diff(y(x),x)+g0(x)*y(x)^3+g1(x)*y(x)^2+g2(x)*y(x)+g3(x), y(x),'implicit')
Maple raw output
dsolve(diff(diff(y(x),x),x) = (f0(x)*y(x)+f1(x))*diff(y(x),x)+g0(x)*y(x)^3+g1(x)*y(x)^2+g2(x)*y(x)+g3(x), y(x),'implicit')