64.11.15 problem 15

Internal problem ID [13465]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 05:44:37 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 33

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+4*y(x)=4*exp(x)-18*exp(-x),y(x), singsol=all)
 

\[ y = \frac {\left (-6 x +3 c_{1} -4\right ) {\mathrm e}^{-x}}{3}+\left (c_{3} x +c_{2} \right ) {\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.230 (sec). Leaf size: 78

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+4*y[x]==4*Exp[x]-18*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \int _1^x-\frac {2}{9} e^{-3 K[1]} \left (-9+2 e^{2 K[1]}\right ) (3 K[1]+1)dK[1]-\frac {2}{9} e^x (6 x-1)+c_1 e^{-x}+e^{2 x} (c_3 x+c_2) \]