4.45.49 \(5 y'''(x)+x y''''(x)=0\)

ODE
\[ 5 y'''(x)+x y''''(x)=0 \] ODE Classification

[[_high_order, _missing_y]]

Book solution method
TO DO

Mathematica
cpu = 0.00903929 (sec), leaf count = 27

\[\left \{\left \{y(x)\to c_4 x^2-\frac {c_1}{24 x^2}+c_3 x+c_2\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 19

\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\it \_C2}\,x+{\it \_C3}\,{x}^{2}+{\frac {{\it \_C4}}{{x}^{2}}} \right \} \] Mathematica raw input

DSolve[5*y'''[x] + x*y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -C[1]/(24*x^2) + C[2] + x*C[3] + x^2*C[4]}}

Maple raw input

dsolve(x*diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(diff(y(x),x),x),x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1+_C2*x+_C3*x^2+_C4/x^2