ODE
\[ x^3 y'''(x)+3 x^2 y''(x)=a \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0160316 (sec), leaf count = 26
\[\left \{\left \{y(x)\to -a \log (x)+\frac {c_1}{2 x}+c_3 x+c_2\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{2\,x}}-a\ln \left ( x \right ) +{\it \_C2}\,x+{\it \_C3} \right \} \] Mathematica raw input
DSolve[3*x^2*y''[x] + x^3*y'''[x] == a,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/(2*x) + C[2] + x*C[3] - a*Log[x]}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x) = a, y(x),'implicit')
Maple raw output
y(x) = 1/2*_C1/x-a*ln(x)+_C2*x+_C3