15.10.17 problem 17

Internal problem ID [3104]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 17
Date solved : Monday, January 27, 2025 at 07:19:29 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 32

dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)-6*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 114

DSolve[D[y[x],{x,4}]-2*D[y[x],{x,3}]-6*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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