Internal problem ID [5067]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 2. Linear homogeneous equations. Section 2.2 problems. page 95
Problem number: 59.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime \prime \prime }-x^{2} y^{\prime \prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 36
dsolve(x^4*diff(y(x),x$4)-x^2*diff(y(x),x$2)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}x^{\RootOf \left (\textit {\_Z}^{4}-6 \textit {\_Z}^{3}+10 \textit {\_Z}^{2}-5 \textit {\_Z} +1, \mathit {index} =\textit {\_a} \right )} \textit {\_C}_{\textit {\_a}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 130
DSolve[x^4*y''''[x]-x^2*y''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_4 x^{\text {Root}\left [\text {$\#$1}^4-6 \text {$\#$1}^3+10 \text {$\#$1}^2-5 \text {$\#$1}+1\&,4\right ]}+c_3 x^{\text {Root}\left [\text {$\#$1}^4-6 \text {$\#$1}^3+10 \text {$\#$1}^2-5 \text {$\#$1}+1\&,3\right ]}+c_1 x^{\text {Root}\left [\text {$\#$1}^4-6 \text {$\#$1}^3+10 \text {$\#$1}^2-5 \text {$\#$1}+1\&,1\right ]}+c_2 x^{\text {Root}\left [\text {$\#$1}^4-6 \text {$\#$1}^3+10 \text {$\#$1}^2-5 \text {$\#$1}+1\&,2\right ]} \\ \end{align*}