73.15.3 problem 22.1 (c)

Internal problem ID [15434]
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 : 22.1 (c)
Date solved : Tuesday, January 28, 2025 at 07:55:33 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=30 \,{\mathrm e}^{-4 x} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+4*diff(y(x),x)-5*y(x)=30*exp(-4*x),y(x), singsol=all)
 

\[ y = \left ({\mathrm e}^{6 x} c_{2} -6 \,{\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-5 x} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]+4*D[y[x],x]-5*y[x]==30*Exp[-4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-5 x} \left (-6 e^x+c_2 e^{6 x}+c_1\right ) \]