44.5.49 problem 45

Internal problem ID [7111]
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 : 45
Date solved : Sunday, March 30, 2025 at 11:42:46 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\left (y-1\right )^{2}+\frac {1}{100} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.068 (sec). Leaf size: 12

ode:=diff(y(x),x) = (-1+y(x))^2+1/100; 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 1+\frac {\tan \left (\frac {x}{10}\right )}{10} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 17

ode=D[y[x],x]==(y[x]-1)^2+1/100; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{10} \tan \left (\frac {x}{10}\right )+1 \]

✓ Sympy. Time used: 0.384 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(y(x) - 1)**2 + Derivative(y(x), x) - 1/100,0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\tan {\left (\frac {x}{10} \right )}}{10} + 1 \]