4.41.20 \(2 (1-y(x)) y(x) y''(x)=4 y(x) y'(x) (f(x)+g(x) y(x))+(1-3 y(x)) y'(x)^2\)

ODE
\[ 2 (1-y(x)) y(x) y''(x)=4 y(x) y'(x) (f(x)+g(x) y(x))+(1-3 y(x)) y'(x)^2 \] ODE Classification

[NONE]

Book solution method
TO DO

Mathematica
cpu = 0.492019 (sec), leaf count = 0 , could not solve

DSolve[2*(1 - y[x])*y[x]*Derivative[2][y][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 = 0.623 (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), y(x),'implicit')

Mathematica raw input

DSolve[2*(1 - y[x])*y[x]*y''[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] == 4*y[x]*(f[x] + g[x]*y[x])*Deriva
tive[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), 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), y(x),'implicit')