Internal problem ID [5536]
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(c).
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 }+9 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 11
dsolve([diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=0,y(0) = 0, D(y)(0) = 5],y(x), singsol=all)
\[ y \relax (x ) = 5 \,{\mathrm e}^{3 x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 13
DSolve[{y''[x]-6*y'[x]+9*y[x]==0,{y[0]==0,y'[0]==5}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 5 e^{3 x} x \\ \end{align*}