44.5.55 problem 48 (b 1)

Internal problem ID [7117]
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 1)
Date solved : Sunday, March 30, 2025 at 11:43:06 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 13

ode:=diff(y(x),x) = 1/(y(x)-3); 
ic:=y(0) = 4; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 16

ode=D[y[x],x]==1/(y[x]-3); 
ic={y[0]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.341 (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(0): 4} 
dsolve(ode,func=y(x),ics=ics)
 

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