ODE
\[ x^2 y'''(x)-2 (n+1) x y''(x)+6 n y'(x)=0 \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.189387 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {c_1 x^{2 n+1}}{2 n+1}+\frac {c_2 x^4}{4}+c_3\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 20
\[[y \left (x \right ) = \textit {\_C1} +\textit {\_C2} \,x^{4}+\textit {\_C3} \,x^{1+2 n}]\] Mathematica raw input
DSolve[6*n*y'[x] - 2*(1 + n)*x*y''[x] + x^2*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^(1 + 2*n)*C[1])/(1 + 2*n) + (x^4*C[2])/4 + C[3]}}
Maple raw input
dsolve(x^2*diff(diff(diff(y(x),x),x),x)-2*(n+1)*x*diff(diff(y(x),x),x)+6*n*diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = _C1+_C2*x^4+_C3*x^(1+2*n)]