71.8.28 problem 10 (b)

Internal problem ID [14462]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 10 (b)
Date solved : Tuesday, January 28, 2025 at 06:37:39 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sqrt {\left (y+2\right ) \left (y-1\right )} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 5

dsolve([diff(y(x),x)=sqrt( (y(x)+2)*( y(x)-1)),y(0) = 1],y(x), singsol=all)
 

\[ y = 1 \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 23

DSolve[{D[y[x],x]==Sqrt[ (y[x]+2)*( y[x]-1)],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (3 e^{-x}+3 e^x-2\right ) \]