Internal problem ID [5535]
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 2.1. Linear Equations with Constant
Coefficients. Page 62
Problem number: 2(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+5 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3, y^{\prime }\relax (0) = 11] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 13
dsolve([diff(y(x),x$2)-6*diff(y(x),x)+5*y(x)=0,y(0) = 3, D(y)(0) = 11],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x}+2 \,{\mathrm e}^{5 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{y''[x]-5*y'[x]+6*y[x]==0,{y[0]==3,y'[0]==11}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} \left (5 e^x-2\right ) \\ \end{align*}