78.12.3 problem 1 (c)

Internal problem ID [18290]
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 (c)
Date solved : Tuesday, January 28, 2025 at 11:45:16 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 30

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

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