Internal problem ID [2147]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 8.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime \prime }-y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 28
dsolve(diff(y(x),x$4)-y(x)=exp(x),y(x), singsol=all)
\[ y = \frac {x \,{\mathrm e}^{x}}{4}+\cos \left (x \right ) c_{1} +c_{2} {\mathrm e}^{x}+c_{3} \sin \left (x \right )+c_{4} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 45
DSolve[y''''[x]-y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x x}{4}-\frac {3 e^x}{8}+c_1 e^x+c_3 e^{-x}+c_2 \cos (x)+c_4 \sin (x) \]