73.14.7 problem 21.9

Internal problem ID [15417]
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 : 21.9
Date solved : Tuesday, January 28, 2025 at 07:55:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{5 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=12\\ y^{\prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=7*exp(5*x),y(0) = 12, D(y)(0) = -2],y(x), singsol=all)
 

\[ y = \left (9+\left (x +3\right ) {\mathrm e}^{7 x}\right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 22

DSolve[{D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==7*Exp[5*x],{y[0]==12,Derivative[1][y][0] ==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (e^{7 x} (x+3)+9\right ) \]