35.6.4 problem 4

Internal problem ID [6154]
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 : 4
Date solved : Monday, January 27, 2025 at 01:38:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=24 \,{\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=24*exp(-3*x),y(x), singsol=all)
 

\[ y = \left (c_2 \,{\mathrm e}^{6 x}+c_1 \,{\mathrm e}^{2 x}+2\right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]-2*D[y[x],x]-3*y[x]==24*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (c_1 e^{2 x}+c_2 e^{6 x}+2\right ) \]