ODE
\[ x^3 y'''(x)+2 x^2 y''(x)+2 y(x)=0 \] ODE Classification
[[_3rd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.158548 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_3}{x}+c_2 x \cos (\log (x))+c_1 x \sin (\log (x))\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 22
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}+\textit {\_C2} x \sin \left (\ln \left (x \right )\right )+\textit {\_C3} x \cos \left (\ln \left (x \right )\right )\right ]\] Mathematica raw input
DSolve[2*y[x] + 2*x^2*y''[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[3]/x + x*C[2]*Cos[Log[x]] + x*C[1]*Sin[Log[x]]}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+2*x^2*diff(diff(y(x),x),x)+2*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/x*_C1+_C2*x*sin(ln(x))+_C3*x*cos(ln(x))]