73.15.5 problem 22.2

Internal problem ID [15436]
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 : 22.2
Date solved : Tuesday, January 28, 2025 at 07:55:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-5 \,{\mathrm e}^{3 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 22

dsolve([diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=-5*exp(3*x),y(0) = 5, D(y)(0) = 3],y(x), singsol=all)
 

\[ y = \frac {\left (3 \,{\mathrm e}^{7 x}+{\mathrm e}^{5 x}+6\right ) {\mathrm e}^{-2 x}}{2} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 28

DSolve[{D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==-5*Exp[3*x],{y[0]==5,Derivative[1][y][0] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-2 x} \left (e^{5 x}+3 e^{7 x}+6\right ) \]