4.39.4 \(y(x) y''(x)=e^x y(x) \left (\text {a0}+\text {a1} y(x)^2\right )+e^{2 x} \left (\text {a2}+\text {a3} y(x)^4\right )+y'(x)^2\)

ODE
\[ y(x) y''(x)=e^x y(x) \left (\text {a0}+\text {a1} y(x)^2\right )+e^{2 x} \left (\text {a2}+\text {a3} y(x)^4\right )+y'(x)^2 \] ODE Classification

[NONE]

Book solution method
TO DO

Mathematica
cpu = 5.62937 (sec), leaf count = 0 , could not solve

DSolve[y[x]*Derivative[2][y][x] == E^x*y[x]*(a0 + a1*y[x]^2) + E^(2*x)*(a2 + a3*y[x]^4) + Derivative[1][y][x]^2, y[x], x]

Maple
cpu = 4.024 (sec), leaf count = 0 , could not solve

dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+exp(x)*y(x)*(a0+a1*y(x)^2)+exp(2*x)*(a2+a3*y(x)^4), y(x),'implicit')

Mathematica raw input

DSolve[y[x]*y''[x] == E^x*y[x]*(a0 + a1*y[x]^2) + E^(2*x)*(a2 + a3*y[x]^4) + y'[x]^2,y[x],x]

Mathematica raw output

DSolve[y[x]*Derivative[2][y][x] == E^x*y[x]*(a0 + a1*y[x]^2) + E^(2*x)*(a2 + a3*
y[x]^4) + 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+exp(x)*y(x)*(a0+a1*y(x)^2)+exp(2*x)*(a2+a3*y(x)^4), y(x),'implicit')

Maple raw output

dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+exp(x)*y(x)*(a0+a1*y(x)^2)+exp
(2*x)*(a2+a3*y(x)^4), y(x),'implicit')