73.15.22 problem 22.8

Internal problem ID [15453]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.8
Date solved : Tuesday, January 28, 2025 at 07:56:23 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=39 x \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 30

dsolve([diff(y(x),x$2)+9*y(x)=39*x*exp(2*x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{2 x} x -\frac {5 \sin \left (3 x \right )}{13}+\frac {25 \cos \left (3 x \right )}{13}-\frac {12 \,{\mathrm e}^{2 x}}{13} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 34

DSolve[{D[y[x],{x,2}]+9*y[x]==39*x*Exp[2*x],{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{13} \left (3 e^{2 x} (13 x-4)-5 \sin (3 x)+25 \cos (3 x)\right ) \]