50.9.19 problem 2(a)

Internal problem ID [7955]
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)
Date solved : Monday, January 27, 2025 at 03:33:55 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (1\right )&={\mathrm e}^{2}\\ y^{\prime }\left (1\right )&=3 \,{\mathrm e}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 10

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)
 

\[ y = {\mathrm e}^{3 x -1} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 12

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

\[ y(x)\to e^{3 x-1} \]