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 = 0.167681 (sec), leaf count = 35
\[\left \{\left \{y(x)\to \frac {1}{4} (2 c_1-c_2) x^2+\frac {1}{2} c_2 x^2 \log (x)+c_3\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 18
\[[y \left (x \right ) = \textit {\_C1} +x^{2} \textit {\_C2} +\textit {\_C3} \,x^{2} \ln \left (x \right )]\] 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] + (x^2*C[2]*Log[x])/2}}
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))
Maple raw output
[y(x) = _C1+x^2*_C2+_C3*x^2*ln(x)]