60.1.57 problem 57

Internal problem ID [10071]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 57
Date solved : Monday, January 27, 2025 at 06:21:47 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-\sqrt {{| y|}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 29

dsolve(diff(y(x),x) - sqrt(abs(y(x)))=0,y(x), singsol=all)
 

\[ x +2 \left (\left \{\begin {array}{cc} \sqrt {-y} & y\le 0 \\ -\sqrt {y} & 0<y \end {array}\right .\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.211 (sec). Leaf size: 31

DSolve[D[y[x],x] - Sqrt[Abs[y[x]]]==0,y[x],x,IncludeSingularSolutions -> True]
 

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