32.1.2 problem 2

Internal problem ID [7707]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Test excercise 24. page 1067
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 04:56:20 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.202 (sec). Leaf size: 47

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+1}dK[1]\&\right ]\left [-\frac {1}{x+1}+c_1\right ]\\ y(x)&\to -i\\ y(x)&\to i \end{align*}

✓ Sympy. Time used: 0.235 (sec). Leaf size: 14

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

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