ODE
\[ x^3 y'''(x)-x^2 y''(x)+x y'(x)=0 \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.016303 (sec), leaf count = 36
\[\left \{\left \{y(x)\to \frac {1}{4} \left (\left (2 c_1-c_2\right ) x^2+2 c_2 x^2 \log (x)+4 c_3\right )\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\it \_C2}\,{x}^{2}+{\it \_C3}\,{x}^{2}\ln \left ( x \right ) \right \} \] Mathematica raw input
DSolve[x*y'[x] - x^2*y''[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^2*(2*C[1] - C[2]) + 4*C[3] + 2*x^2*C[2]*Log[x])/4}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)-x^2*diff(diff(y(x),x),x)+x*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1+_C2*x^2+_C3*x^2*ln(x)