ODE
\[ 2 (1-y(x)) y(x) y''(x)=-4 y(x)^2 (1-y(x)) \left (f'(x)+f(x)^2+g'(x)-g(x)^2\right )-4 y(x) y'(x) (f(x)+g(x) y(x))+(1-y(x))^3 \left (-\left (\text {F0}(x)^2-\text {G0}(x)^2 y(x)^2\right )\right )+(1-3 y(x)) y'(x)^2 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 10.4889 (sec), leaf count = 0 , could not solve
DSolve[2*(1 - y[x])*y[x]*Derivative[2][y][x] == -((1 - y[x])^3*(F0[x]^2 - G0[x]^2*y[x]^2)) - 4*(1 - y[x])*y[x]^2*(f[x]^2 - g[x]^2 + Derivative[1][f][x] + Derivative[1][g][x]) - 4*y[x]*(f[x] + g[x]*y[x])*Derivative[1][y][x] + (1 - 3*y[x])*Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 12.776 (sec), leaf count = 0 , could not solve
dsolve(2*y(x)*(1-y(x))*diff(diff(y(x),x),x) = (1-3*y(x))*diff(y(x),x)^2-4*y(x)*(f(x)+g(x)*y(x))*diff(y(x),x)-(1-y(x))^3*(F0(x)^2-G0(x)^2*y(x)^2)-4*(1-y(x))*y(x)^2*(f(x)^2+diff(f(x),x)-g(x)^2+diff(g(x),x)), y(x),'implicit')
Mathematica raw input
DSolve[2*(1 - y[x])*y[x]*y''[x] == -((1 - y[x])^3*(F0[x]^2 - G0[x]^2*y[x]^2)) - 4*(1 - y[x])*y[x]^2*(f[x]^2 - g[x]^2 + f'[x] + g'[x]) - 4*y[x]*(f[x] + g[x]*y[x])*y'[x] + (1 - 3*y[x])*y'[x]^2,y[x],x]
Mathematica raw output
DSolve[2*(1 - y[x])*y[x]*Derivative[2][y][x] == -((1 - y[x])^3*(F0[x]^2 - G0[x]^2*y[x]^2)) - 4*(1 - y[x])*y[x]^2*(f[x]^2 - g[x]^2 + Derivative[1][f][x] + Derivative[1][g][x]) - 4*y[x]*(f[x] + g[x]*y[x])*Derivative[1][y][x] + (1 - 3*y[x])*Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(2*y(x)*(1-y(x))*diff(diff(y(x),x),x) = (1-3*y(x))*diff(y(x),x)^2-4*y(x)*(f(x)+g(x)*y(x))*diff(y(x),x)-(1-y(x))^3*(F0(x)^2-G0(x)^2*y(x)^2)-4*(1-y(x))*y(x)^2*(f(x)^2+diff(f(x),x)-g(x)^2+diff(g(x),x)), y(x),'implicit')
Maple raw output
dsolve(2*y(x)*(1-y(x))*diff(diff(y(x),x),x) = (1-3*y(x))*diff(y(x),x)^2-4*y(x)*(f(x)+g(x)*y(x))*diff(y(x),x)-(1-y(x))^3*(F0(x)^2-G0(x)^2*y(x)^2)-4*(1-y(x))*y(x)^2*(f(x)^2+diff(f(x),x)-g(x)^2+diff(g(x),x)), y(x),'implicit')