ODE
\[ y''(x)=x^{n-2} f\left (x^{-n} y(x),x^{1-n} y'(x)\right ) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 6.51516 (sec), leaf count = 0 , could not solve
DSolve[Derivative[2][y][x] == x^(-2 + n)*f[y[x]/x^n, x^(1 - n)*Derivative[1][y][x]], y[x], x]
Maple ✗
cpu = 1.349 (sec), leaf count = 0 , result contains DESol or ODESolStruc
\[[]\]
Mathematica raw input
DSolve[y''[x] == x^(-2 + n)*f[y[x]/x^n, x^(1 - n)*y'[x]],y[x],x]
Mathematica raw output
DSolve[Derivative[2][y][x] == x^(-2 + n)*f[y[x]/x^n, x^(1 - n)*Derivative[1][y][x]], y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x) = x^(n-2)*f(y(x)/(x^n),diff(y(x),x)/(x^(n-1))), y(x))
Maple raw output
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