71.8.27 problem 10 (a)

Internal problem ID [14390]
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 (a)
Date solved : Monday, March 31, 2025 at 12:22:53 PM
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 )&=0 \end{align*}

✓ Maple. Time used: 0.433 (sec). Leaf size: 17

ode:=diff(y(x),x) = ((2+y(x))*(-1+y(x)))^(1/2); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {1}{2}+\frac {\cosh \left (x \right )}{2}+i \sqrt {2}\, \sinh \left (x \right ) \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 45

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt((y(x) - 1)*(y(x) + 2)) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants