78.12.19 problem 2 (a)

Internal problem ID [18306]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 2 (a)
Date solved : Tuesday, January 28, 2025 at 11:45:48 AM
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: 0.025 (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: 0.013 (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]
 

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