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 = 0.010477 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_3}{x}+c_1 x \sin (\log (x))+c_2 x \cos (\log (x))\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\,{x}^{2}\sin \left ( \ln \left ( x \right ) \right ) +{\it \_C3}\,{x}^{2}\cos \left ( \ln \left ( x \right ) \right ) +{\it \_C1}}{x}} \right \} \] 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),'implicit')
Maple raw output
y(x) = (_C2*x^2*sin(ln(x))+_C3*x^2*cos(ln(x))+_C1)/x