Internal problem ID [5534]
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(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = {\mathrm e}^{2}, y^{\prime }\relax (1) = 3 \,{\mathrm e}^{2}] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 11
dsolve([diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=0,y(1) = exp(2), D(y)(1) = 3*exp(2)],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{3 x -1} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 12
DSolve[{y''[x]-5*y'[x]+6*y[x]==0,{y[1]==Exp[2],y'[1]==3*Exp[2]}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{3 x-1} \\ \end{align*}