15.11.8 problem 8

Internal problem ID [3118]
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
Date solved : Monday, January 27, 2025 at 07:21:00 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

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

\[ y = c_4 \,{\mathrm e}^{-x}+\frac {\left (4 c_2 +x \right ) {\mathrm e}^{x}}{4}+\cos \left (x \right ) c_{1} +c_3 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 45

DSolve[D[y[x],{x,4}]-y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

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