ODE
\[ x^3 y'''(x)=a \] ODE Classification
[[_3rd_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00815229 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {1}{2} a \log (x)+x \left (c_3 x+c_2\right )+c_1\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\frac {a\ln \left ( x \right ) }{2}}+{\frac {{\it \_C1}\,{x}^{2}}{2}}+{\it \_C2}\,x+{\it \_C3} \right \} \] Mathematica raw input
DSolve[x^3*y'''[x] == a,y[x],x]
Mathematica raw output
{{y[x] -> C[1] + x*(C[2] + x*C[3]) + (a*Log[x])/2}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x) = a, y(x),'implicit')
Maple raw output
y(x) = 1/2*a*ln(x)+1/2*_C1*x^2+_C2*x+_C3