35.6.8 problem 8

Internal problem ID [6158]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 8
Date solved : Monday, January 27, 2025 at 01:38:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-16 y&=40 \,{\mathrm e}^{4 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)-16*y(x)=40*exp(4*x),y(x), singsol=all)
 

\[ y = \left (5 x +c_1 \right ) {\mathrm e}^{4 x}+{\mathrm e}^{-4 x} c_2 \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]-16*y[x]==40*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{4 x} \left (5 x-\frac {5}{8}+c_1\right )+c_2 e^{-4 x} \]