Internal problem ID [2133]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}-6 \textit {\_Z} +2, \operatorname {index} =\textit {\_a} \right ) x} \textit {\_C}_{\textit {\_a}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 114
DSolve[y''''[x]-2*y'''[x]-6*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3-6 \text {$\#$1}+2\&,1\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3-6 \text {$\#$1}+2\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3-6 \text {$\#$1}+2\&,4\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3-6 \text {$\#$1}+2\&,2\right ]\right ) \]