4.29.43 \(x^2 y''(x)-x y'(x)+2 y(x)=0\)

ODE
\[ x^2 y''(x)-x y'(x)+2 y(x)=0 \] ODE Classification

[[_Emden, _Fowler]]

Book solution method
TO DO

Mathematica
cpu = 0.0117796 (sec), leaf count = 20

\[\left \{\left \{y(x)\to x \left (c_1 \sin (\log (x))+c_2 \cos (\log (x))\right )\right \}\right \}\]

Maple
cpu = 0.005 (sec), leaf count = 17

\[ \left \{ y \left ( x \right ) =x \left ( \sin \left ( \ln \left ( x \right ) \right ) {\it \_C1}+\cos \left ( \ln \left ( x \right ) \right ) {\it \_C2} \right ) \right \} \] Mathematica raw input

DSolve[2*y[x] - x*y'[x] + x^2*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> x*(C[2]*Cos[Log[x]] + C[1]*Sin[Log[x]])}}

Maple raw input

dsolve(x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+2*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = x*(sin(ln(x))*_C1+cos(ln(x))*_C2)