50.9.20 problem 2(b)

Internal problem ID [7956]
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)
Date solved : Monday, January 27, 2025 at 03:33:57 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=11 \end{align*}

✓ Solution by Maple

Time used: 0.010 (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)
 

\[ y = {\mathrm e}^{x}+2 \,{\mathrm e}^{5 x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==0,{y[0]==3,Derivative[1][y][0] ==11}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (5 e^x-2\right ) \]