15.14.9 problem 9

Internal problem ID [3181]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 9
Date solved : Monday, January 27, 2025 at 07:25:17 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 40

dsolve(diff(y(x),x$3)-y(x)=exp(x),y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+\frac {{\mathrm e}^{x} \left (x +3 c_{1} \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.400 (sec). Leaf size: 62

DSolve[D[y[x],{x,3}]-y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{-x/2} \left (e^{3 x/2} (x-1+3 c_1)+3 c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+3 c_3 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \]