Internal problem ID [2130]
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: 14.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime }-20 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$4)+diff(y(x),x$2)-20*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{-2 x} c_{2} +c_{3} \sin \left (\sqrt {5}\, x \right )+c_{4} \cos \left (\sqrt {5}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 44
DSolve[y''''[x]+y''[x]-20*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 e^{-2 x}+c_4 e^{2 x}+c_1 \cos \left (\sqrt {5} x\right )+c_2 \sin \left (\sqrt {5} x\right ) \]