73.14.8 problem 21.10

Internal problem ID [15418]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.10
Date solved : Tuesday, January 28, 2025 at 07:55:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=169 \sin \left (2 x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-10\\ y^{\prime }\left (0\right )&=9 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 27

dsolve([diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=169*sin(2*x),y(0) = -10, D(y)(0) = 9],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 34

DSolve[{D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==169*Sin[2*x],{y[0]==-10,Derivative[1][y][0] ==9}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (5 x+5 e^{3 x} \sin (2 x)+2\right )-12 \cos (2 x) \]