67.1.2 problem Problem 1(b)

Internal problem ID [13878]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 2, First Order Equations. Problems page 149
Problem number : Problem 1(b)
Date solved : Monday, March 31, 2025 at 08:16:00 AM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime }&=1+y^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=x^2*diff(y(x),x) = 1+y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \tan \left (\frac {c_1 x -1}{x}\right ) \]

✓ Mathematica. Time used: 0.229 (sec). Leaf size: 30

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

\begin{align*} y(x)\to \tan \left (\frac {-1+c_1 x}{x}\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}

✓ Sympy. Time used: 0.295 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = \tan {\left (C_{1} - \frac {1}{x} \right )} \]