ODE
\[ x^2 y'''(x)+2 x y''(x)=a \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0142653 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \log (x) \left (a x-c_1\right )-a x+c_3 x+c_2\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) = \left ( ax-{\it \_C1} \right ) \ln \left ( x \right ) + \left ( -a+{\it \_C2} \right ) x+{\it \_C3} \right \} \] 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),'implicit')
Maple raw output
y(x) = (a*x-_C1)*ln(x)+(-a+_C2)*x+_C3