76.5.19 problem 19

Internal problem ID [17439]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 10:37:36 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(diff(y(t),t)=y(t)+sqrt(y(t)),y(t), singsol=all)
 

\[ 1-{\mathrm e}^{\frac {t}{2}} c_{1} +\sqrt {y} = 0 \]

✓ Solution by Mathematica

Time used: 0.189 (sec). Leaf size: 29

DSolve[D[y[t],t]==y[t]+Sqrt[ y[t] ],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \left (-1+e^{\frac {t+c_1}{2}}\right ){}^2 \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}