64.11.7 problem 7

Internal problem ID [13457]
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 : 7
Date solved : Tuesday, January 28, 2025 at 05:44:16 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+5 y&=2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+5*y(x)=2*exp(x)+10*exp(5*x),y(x), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{10 x}+{\mathrm e}^{6 x}+6 \,{\mathrm e}^{4 x} c_{1} +6 c_{2} \right ) {\mathrm e}^{-5 x}}{6} \]

✓ Solution by Mathematica

Time used: 0.231 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+5*y[x]==2*Exp[x]+10*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^x \left (e^{4 x}+1\right )+c_1 e^{-5 x}+c_2 e^{-x} \]