78.12.6 problem 1 (f)

Internal problem ID [18293]
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 : 1 (f)
Date solved : Tuesday, January 28, 2025 at 11:45:23 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+20 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)-9*diff(y(x),x)+20*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{4 x}+c_{2} {\mathrm e}^{5 x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}] -9*D[y[x],x]+20*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{4 x} \left (c_2 e^x+c_1\right ) \]