34.3.28 problem 26 (b)

Internal problem ID [7919]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 26 (b)
Date solved : Tuesday, September 30, 2025 at 05:10:03 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 15

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

\[ y = \tan \left (-\ln \left (x +1\right )+\ln \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.167 (sec). Leaf size: 56

ode=1+y[x]^2==(x+x^2)*D[y[x],x]; 
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 [\int _1^x\frac {1}{K[2]^2+K[2]}dK[2]+c_1\right ]\\ y(x)&\to -i\\ y(x)&\to i \end{align*}

✓ Sympy. Time used: 0.379 (sec). Leaf size: 14

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

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