4.37.40 \(y''(x)=f\left (a x+b y(x),y'(x)\right )\)

ODE
\[ y''(x)=f\left (a x+b y(x),y'(x)\right ) \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.51903 (sec), leaf count = 0 , could not solve

DSolve[Derivative[2][y][x] == f[a*x + b*y[x], Derivative[1][y][x]], y[x], x]

Maple
cpu = 0.502 (sec), leaf count = 0 , result contains DESol or ODESolStruc

\[[]\]

Mathematica raw input

DSolve[y''[x] == f[a*x + b*y[x], y'[x]],y[x],x]

Mathematica raw output

DSolve[Derivative[2][y][x] == f[a*x + b*y[x], Derivative[1][y][x]], y[x], x]

Maple raw input

dsolve(diff(diff(y(x),x),x) = f(a*x+b*y(x),diff(y(x),x)), y(x))

Maple raw output

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