78.1.46 problem 6

Internal problem ID [18101]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 11:26:21 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} c_{1} +{\mathrm e}^{2 x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

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

\[ y(x)\to e^{2 x} \left (c_2 e^x+c_1\right ) \]