72.3.11 problem 15

Internal problem ID [14675]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.4 page 61
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 06:47:23 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 11

dsolve([diff(y(t),t)=sqrt( y(t)),y(0) = 1],y(t), singsol=all)
 

\[ y = \frac {\left (t +2\right )^{2}}{4} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 14

DSolve[{D[y[t],t]==Sqrt[ y[t] ],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{4} (t+2)^2 \]