20.2.16 problem Problem 16

Internal problem ID [3608]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations. page 43
Problem number : Problem 16
Date solved : Sunday, March 30, 2025 at 01:54:25 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {2 \sqrt {y-1}}{3} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 5

ode:=diff(y(x),x) = 2/3*(-1+y(x))^(1/2); 
ic:=y(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 1 \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 17

ode=D[y[x],x]==1/3*(y[x]-1)^(1/2); 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{36} \left (x^2-2 x+37\right ) \]

✓ Sympy. Time used: 0.224 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*sqrt(y(x) - 1)/3 + Derivative(y(x), x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{2}}{9} - \frac {2 x}{9} + \frac {10}{9} \]