64.11.32 problem 32

Internal problem ID [13482]
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 : 32
Date solved : Tuesday, January 28, 2025 at 05:45:11 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+29 y&=8 \,{\mathrm e}^{5 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 22

dsolve([diff(y(x),x$2)-10*diff(y(x),x)+29*y(x)=8*exp(5*x),y(0) = 0, D(y)(0) = 8],y(x), singsol=all)
 

\[ y = -2 \,{\mathrm e}^{5 x} \left (-1-2 \sin \left (2 x \right )+\cos \left (2 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 24

DSolve[{D[y[x],{x,2}]-10*D[y[x],x]+29*y[x]==8*Exp[5*x],{y[0]==0,Derivative[1][y][0] ==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 e^{5 x} (-2 \sin (2 x)+\cos (2 x)-1) \]