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')