71.4.5 problem 5

Internal problem ID [14377]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 06:28:14 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 30

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

\[ x +\ln \left (2\right )-\ln \left (2 y+1+2 \sqrt {\left (y+2\right ) \left (y-1\right )}\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.271 (sec). Leaf size: 41

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

\begin{align*} y(x)\to \frac {1}{4} \left (-e^{-x-c_1}-9 e^{x+c_1}-2\right ) \\ y(x)\to -2 \\ y(x)\to 1 \\ \end{align*}