56.3.20 problem 20

Internal problem ID [8878]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 20
Date solved : Monday, January 27, 2025 at 05:11:36 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} 5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (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)
 

\[ y = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}x^{\operatorname {RootOf}\left (5 \textit {\_Z}^{4}-26 \textit {\_Z}^{3}+43 \textit {\_Z}^{2}-21 \textit {\_Z} +1, \operatorname {index} =\textit {\_a} \right )} \textit {\_C}_{\textit {\_a}} \]

✓ Solution by Mathematica

Time used: 1.457 (sec). Leaf size: 1931

DSolve[5*x^5*D[y[x],{x,4}]+4*x^4*D[y[x],{x,3}]+x^2*D[y[x],x]+x*y[x]== Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

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