ODE
\[ x y(x) y''(x)=x \left (\text {a0}+\text {a1} y(x)^4\right )+y(x) \left (\text {a2}+\text {a3} y(x)^2\right )+x y'(x)^2-y(x) y'(x) \] ODE Classification
[[_Painleve, `3rd`]]
Book solution method
TO DO
Mathematica ✗
cpu = 1.57506 (sec), leaf count = 0 , could not solve
DSolve[x*y[x]*Derivative[2][y][x] == y[x]*(a2 + a3*y[x]^2) + x*(a0 + a1*y[x]^4) - y[x]*Derivative[1][y][x] + x*Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 0.762 (sec), leaf count = 0 , could not solve
dsolve(x*y(x)*diff(diff(y(x),x),x) = x*diff(y(x),x)^2-y(x)*diff(y(x),x)+x*(a0+a1*y(x)^4)+y(x)*(a2+a3*y(x)^2), y(x),'implicit')
Mathematica raw input
DSolve[x*y[x]*y''[x] == y[x]*(a2 + a3*y[x]^2) + x*(a0 + a1*y[x]^4) - y[x]*y'[x] + x*y'[x]^2,y[x],x]
Mathematica raw output
DSolve[x*y[x]*Derivative[2][y][x] == y[x]*(a2 + a3*y[x]^2) + x*(a0 + a1*y[x]^4) - y[x]*Derivative[1][y][x] + x*Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(x*y(x)*diff(diff(y(x),x),x) = x*diff(y(x),x)^2-y(x)*diff(y(x),x)+x*(a0+a1*y(x)^4)+y(x)*(a2+a3*y(x)^2), y(x),'implicit')
Maple raw output
dsolve(x*y(x)*diff(diff(y(x),x),x) = x*diff(y(x),x)^2-y(x)*diff(y(x),x)+x*(a0+a1*y(x)^4)+y(x)*(a2+a3*y(x)^2), y(x),'implicit')