4.1778   y′′(x) = a+ 2y(x)3 + xy(x)

ODE

y′′(x) = a + 2y(x)3 + xy(x)

ODE Classification

[[_Painleve, `2nd`]]

Book solution method
TO DO

Mathematica
cpu = 1.10058 (sec), leaf count = 0 , could not solve

DSolve[Derivative[2][y][x] == a + x*y[x] + 2*y[x]^3, y[x], x]

Maple
cpu = 0.313 (sec), leaf count = 0 , could not solve

dsolve(diff(diff(y(x),x),x) = a+x*y(x)+2*y(x)^3, y(x),'implicit')

Mathematica raw input

DSolve[y''[x] == a + x*y[x] + 2*y[x]^3,y[x],x]

Mathematica raw output

DSolve[Derivative[2][y][x] == a + x*y[x] + 2*y[x]^3, y[x], x]

Maple raw input

dsolve(diff(diff(y(x),x),x) = a+x*y(x)+2*y(x)^3, y(x),'implicit')

Maple raw output

dsolve(diff(diff(y(x),x),x) = a+x*y(x)+2*y(x)^3, y(x),'implicit')