78.1.4 problem 1 (d)

Internal problem ID [18059]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (d)
Date solved : Tuesday, January 28, 2025 at 11:23:37 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 10

dsolve(diff(y(x),x)=k*y(x),y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{k x} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 18

DSolve[D[y[x],x]==k*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{k x} \\ y(x)\to 0 \\ \end{align*}