47.4.11 problem 59

Internal problem ID [7488]
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
Date solved : Monday, January 27, 2025 at 03:02:05 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }-x^{2} y^{\prime \prime }+y&=0 \end{align*}

✓ 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)
 

\[ y = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}x^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-6 \textit {\_Z}^{3}+10 \textit {\_Z}^{2}-5 \textit {\_Z} +1, \operatorname {index} =\textit {\_a} \right )} \textit {\_C}_{\textit {\_a}} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 130

DSolve[x^4*D[y[x],{x,4}]-x^2*D[y[x],{x,2}]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_4 x^{\text {Root}\left [\text {$\#$1}^4-6 \text {$\#$1}^3+10 \text {$\#$1}^2-5 \text {$\#$1}+1\&,4\right ]}+c_3 x^{\text {Root}\left [\text {$\#$1}^4-6 \text {$\#$1}^3+10 \text {$\#$1}^2-5 \text {$\#$1}+1\&,3\right ]}+c_1 x^{\text {Root}\left [\text {$\#$1}^4-6 \text {$\#$1}^3+10 \text {$\#$1}^2-5 \text {$\#$1}+1\&,1\right ]}+c_2 x^{\text {Root}\left [\text {$\#$1}^4-6 \text {$\#$1}^3+10 \text {$\#$1}^2-5 \text {$\#$1}+1\&,2\right ]} \]