Internal problem ID [4302]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-3 y-24 \,{\mathrm e}^{-3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{3 x}+2 \,{\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 29
DSolve[y''[x]-2*y'[x]-3*y[x]==24*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (c_1 e^{2 x}+c_2 e^{6 x}+2\right ) \\ \end{align*}