3.18 problem 13

Internal problem ID [12632]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

\[ \boxed {y^{\prime }-{| y|}=0} \]

✓ Solution by Maple

Time used: 0.125 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.229 (sec). Leaf size: 29

DSolve[y'[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*}