7.2.17 problem 19

Internal problem ID [35]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.3. Problems at page 27
Problem number : 19
Date solved : Tuesday, March 04, 2025 at 10:39:37 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

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

\[ y(x)\to 0 \]

✓ Sympy. Time used: 0.475 (sec). Leaf size: 22

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

\[ \int \limits ^{y{\left (x \right )}} \frac {1}{\log {\left (y^{2} + 1 \right )}}\, dy = x + \int \limits ^{0} \frac {1}{\log {\left (y^{2} + 1 \right )}}\, dy \]