71.8.29 problem 10 (c)

Internal problem ID [14463]
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 (c)
Date solved : Tuesday, January 28, 2025 at 06:37:44 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 )&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.464 (sec). Leaf size: 16

dsolve([diff(y(x),x)=sqrt( (y(x)+2)*( y(x)-1)),y(0) = -3],y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{x}}{4}-\frac {1}{2}-\frac {9 \,{\mathrm e}^{-x}}{4} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 23

DSolve[{D[y[x],x]==Sqrt[ (y[x]+2)*( y[x]-1)],{y[0]==-3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (-9 e^{-x}-e^x-2\right ) \]