71.3.18 problem 13

Internal problem ID [14368]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 06:27:52 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.273 (sec). Leaf size: 19

dsolve(diff(y(x),x)=abs(y(x)),y(x), singsol=all)
 

\begin{align*} y &= \frac {{\mathrm e}^{-x}}{c_{1}} \\ y &= {\mathrm e}^{x} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{| K[1]| }dK[1]\&\right ][x+c_1] \\ y(x)\to 0 \\ \end{align*}