ODE
\[ f\left (y''(x),y'(x)-x y''(x),\frac {1}{2} x^2 y''(x)-x y'(x)+y(x)\right )=0 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 0.16471 (sec), leaf count = 0 , could not solve
DSolve[f[Derivative[2][y][x], Derivative[1][y][x] - x*Derivative[2][y][x], y[x] - x*Derivative[1][y][x] + (x^2*Derivative[2][y][x])/2] == 0, y[x], x]
Maple ✓
cpu = 0.189 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {x^{2} \RootOf \left (f \left (\textit {\_Z} , \textit {\_C1} , \textit {\_C2}\right )\right )}{2}+\textit {\_C1} x +\textit {\_C2}\right ]\] Mathematica raw input
DSolve[f[y''[x], y'[x] - x*y''[x], y[x] - x*y'[x] + (x^2*y''[x])/2] == 0,y[x],x]
Mathematica raw output
DSolve[f[Derivative[2][y][x], Derivative[1][y][x] - x*Derivative[2][y][x], y[x] - x*Derivative[1][y][x] + (x^2*Derivative[2][y][x])/2] == 0, y[x], x]
Maple raw input
dsolve(f(diff(diff(y(x),x),x),diff(y(x),x)-x*diff(diff(y(x),x),x),y(x)-x*diff(y(x),x)+1/2*x^2*diff(diff(y(x),x),x)) = 0, y(x))
Maple raw output
[y(x) = 1/2*x^2*RootOf(f(_Z,_C1,_C2))+_C1*x+_C2]