ODE
\[ x^2 y'''(x)+2 x y''(x)=a \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.17891 (sec), leaf count = 27
\[\{\{y(x)\to -a x+\log (x) (a x-c_1)+c_3 x+c_2\}\}\]
Maple ✓
cpu = 0.159 (sec), leaf count = 23
\[[y \left (x \right ) = a \ln \left (x \right ) x -a x -\ln \left (x \right ) \textit {\_C1} +\textit {\_C2} x +\textit {\_C3}]\] Mathematica raw input
DSolve[2*x*y''[x] + x^2*y'''[x] == a,y[x],x]
Mathematica raw output
{{y[x] -> -(a*x) + C[2] + x*C[3] + (a*x - C[1])*Log[x]}}
Maple raw input
dsolve(x^2*diff(diff(diff(y(x),x),x),x)+2*x*diff(diff(y(x),x),x) = a, y(x))
Maple raw output
[y(x) = a*ln(x)*x-a*x-ln(x)*_C1+_C2*x+_C3]