78.12.14 problem 1 (n)

Internal problem ID [18301]
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 (n)
Date solved : Tuesday, January 28, 2025 at 11:45:40 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

dsolve(4*diff(y(x),x$2)-8*diff(y(x),x)+7*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 38

DSolve[4*D[y[x],{x,2}] -8*D[y[x],x]+7*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \]