7.11.20 problem 20

Internal problem ID [341]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 20
Date solved : Wednesday, February 05, 2025 at 03:23:48 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{x}+7 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 42

dsolve(diff(y(x),x$3)-y(x)=exp(x)+7,y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )-7+\frac {\left (x +3 c_1 -1\right ) {\mathrm e}^{x}}{3} \]

✓ Solution by Mathematica

Time used: 0.560 (sec). Leaf size: 63

DSolve[D[y[x],{x,3}]-y[x]==Exp[x]+7,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^x (x-1+3 c_1)+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_3 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )-7 \]