11.8 problem 8

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: 0.0 (sec). Leaf size: 28

dsolve(diff(y(x),x$4)-y(x)=exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = c_{4} {\mathrm e}^{-x}+\frac {\left (4 c_{2} +x \right ) {\mathrm e}^{x}}{4}+\cos \left (x \right ) c_{1} +c_{3} \sin \left (x \right ) \]

Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 45

DSolve[y''''[x]-y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x x}{4}-\frac {3 e^x}{8}+c_1 e^x+c_3 e^{-x}+c_2 \cos (x)+c_4 \sin (x) \]