4.44.29 \(x^3 y'''(x)+x y'(x)-y(x)=0\)

ODE
\[ x^3 y'''(x)+x y'(x)-y(x)=0 \] ODE Classification

[[_3rd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.00989205 (sec), leaf count = 22

\[\left \{\left \{y(x)\to x \left (c_3 \log ^2(x)+c_2 \log (x)+c_1\right )\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 18

\[ \left \{ y \left ( x \right ) =x \left ( \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C3}+{\it \_C2}\,\ln \left ( x \right ) +{\it \_C1} \right ) \right \} \] Mathematica raw input

DSolve[-y[x] + x*y'[x] + x^3*y'''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> x*(C[1] + C[2]*Log[x] + C[3]*Log[x]^2)}}

Maple raw input

dsolve(x^3*diff(diff(diff(y(x),x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = x*(ln(x)^2*_C3+_C2*ln(x)+_C1)