78.12.13 problem 1 (m)

Internal problem ID [18300]
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 (m)
Date solved : Tuesday, January 28, 2025 at 11:45:37 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=4 y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)=4*y(x),y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 22

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

\[ y(x)\to e^{-2 x} \left (c_1 e^{4 x}+c_2\right ) \]