78.12.4 problem 1 (d)

Internal problem ID [18291]
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 (d)
Date solved : Tuesday, January 28, 2025 at 11:45:19 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 32

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

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