78.12.10 problem 1 (j)

Internal problem ID [18297]
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 (j)
Date solved : Tuesday, January 28, 2025 at 11:45:31 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+25*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} \left (c_{1} \sin \left (4 x \right )+c_{2} \cos \left (4 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}] -6*D[y[x],x]+25*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} (c_2 \cos (4 x)+c_1 \sin (4 x)) \]