Internal problem ID [5551]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED
COEFFICIENTS. Page 67
Problem number: 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+10 y^{\prime }+25 y-14 \,{\mathrm e}^{-5 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+10*diff(y(x),x)+25*y(x)=14*exp(-5*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-5 x}+x \,{\mathrm e}^{-5 x} c_{1}+7 x^{2} {\mathrm e}^{-5 x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 22
DSolve[y''[x]+10*y'[x]+25*y[x]==14*Exp[-5*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-5 x} (x (7 x+c_2)+c_1) \\ \end{align*}