44.5.57 problem 48 (b 3)

Internal problem ID [7119]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 48 (b 3)
Date solved : Wednesday, March 05, 2025 at 04:12:11 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 15

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

\[ y = 3-\sqrt {-1+2 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 18

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

\[ y(x)\to 3-\sqrt {2 x-1} \]

✓ Sympy. Time used: 0.335 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = 3 - \sqrt {2 x - 1} \]