ODE
\[ x^2 y''''(x)=2 y'''(x) \] ODE Classification
[[_high_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0609586 (sec), leaf count = 62
\[\left \{\left \{y(x)\to \frac {1}{3} c_1 \left (3 x^2+6 x+2\right ) \text {Ei}\left (-\frac {2}{x}\right )+c_4 x^2+\frac {1}{6} c_1 e^{-2/x} \left (x^2+5 x+2\right ) x+c_3 x+c_2\right \}\right \}\]
Maple ✓
cpu = 0.138 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) =-{\it \_C1}\, \left ( {x}^{2}+2\,x+{\frac {2}{3}} \right ) {\it Ei} \left ( 1,2\,{x}^{-1} \right ) +{\frac {x{\it \_C1}\, \left ( {x}^{2}+5\,x+2 \right ) }{6}{{\rm e}^{-2\,{x}^{-1}}}}+{\frac {{\it \_C2}\,{x}^{2}}{2}}+{\it \_C3}\,x+{\it \_C4} \right \} \] Mathematica raw input
DSolve[x^2*y''''[x] == 2*y'''[x],y[x],x]
Mathematica raw output
{{y[x] -> (x*(2 + 5*x + x^2)*C[1])/(6*E^(2/x)) + C[2] + x*C[3] + x^2*C[4] + ((2 + 6*x + 3*x^2)*C[1]*ExpIntegralEi[-2/x])/3}}
Maple raw input
dsolve(x^2*diff(diff(diff(diff(y(x),x),x),x),x) = 2*diff(diff(diff(y(x),x),x),x), y(x),'implicit')
Maple raw output
y(x) = -_C1*(x^2+2*x+2/3)*Ei(1,2/x)+1/6*x*_C1*(x^2+5*x+2)*exp(-2/x)+1/2*_C2*x^2+_C3*x+_C4