73.8.4 problem 13.1 (d)

Internal problem ID [15212]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.1 (d)
Date solved : Tuesday, January 28, 2025 at 07:50:04 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)+2*diff(y(x),x)=8*exp(2*x),y(x), singsol=all)
 

\[ y = -\frac {c_{1} {\mathrm e}^{-2 x}}{2}+{\mathrm e}^{2 x}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]+2*D[y[x],x]==8*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x}-\frac {1}{2} c_1 e^{-2 x}+c_2 \]