Internal problem ID [6457]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 20.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+x y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 38
dsolve(5*x^5*diff(y(x),x$4)+4*x^4*diff(y(x),x$3)+x^2*diff(y(x),x)+x*y(x)= 0,y(x), singsol=all)
\[ y \relax (x ) = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}x^{\RootOf \left (5 \textit {\_Z}^{4}-26 \textit {\_Z}^{3}+43 \textit {\_Z}^{2}-21 \textit {\_Z} +1, \mathit {index} =\textit {\_a} \right )} \textit {\_C}_{\textit {\_a}} \]
✓ Solution by Mathematica
Time used: 1.406 (sec). Leaf size: 1819
DSolve[5*x^5*y''''[x]+4*x^4*y'''[x]+x^2*y'[x]+x*y[x]== Sin[x],y[x],x,IncludeSingularSolutions -> True]
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