73.15.31 problem 22.10 (d)

Internal problem ID [15462]
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 : 22.10 (d)
Date solved : Tuesday, January 28, 2025 at 07:56:45 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{-5 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=6*exp(-5*x),y(x), singsol=all)
 

\[ y = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{5 x}+\frac {3 \,{\mathrm e}^{-5 x}}{50} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 28

DSolve[D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==6*Exp[-5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 e^{-5 x}}{50}+e^{5 x} (c_2 x+c_1) \]