78.12.16 problem 1 (p)

Internal problem ID [18303]
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 (p)
Date solved : Tuesday, January 28, 2025 at 11:45:44 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(16*diff(y(x),x$2)-8*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

DSolve[16*D[y[x],{x,2}] -8*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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