4.44.37 \(x^3 y'''(x)+3 x^2 y''(x)=a\)

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