64.11.16 problem 16

Internal problem ID [13466]
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 : 16
Date solved : Tuesday, January 28, 2025 at 05:44:38 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 32

dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)-diff(y(x),x)+2*y(x)=9*exp(2*x)-8*exp(3*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 44

DSolve[D[y[x],{x,3}]-2*D[y[x],{x,2}]-D[y[x],x]+2*y[x]==9*Exp[2*x]-8*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -e^{3 x}+c_1 e^{-x}+\left (\frac {81}{32}+c_2\right ) e^x+e^{2 x} (3 x-4+c_3) \]