67.7.14 problem 14

Internal problem ID [16459]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 14
Date solved : Thursday, October 02, 2025 at 01:34:06 PM
CAS classification : [_linear]

\begin{align*} 2+2 x^{2}-2 y x +\left (x^{2}+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=2+2*x^2-2*x*y(x)+(x^2+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-2 \arctan \left (x \right )+c_1 \right ) \left (x^{2}+1\right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 0.221 (sec). Leaf size: 42

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

\[ y{\left (x \right )} = C_{1} x^{2} + C_{1} + i x^{2} \log {\left (x - i \right )} - i x^{2} \log {\left (x + i \right )} + i \log {\left (x - i \right )} - i \log {\left (x + i \right )} \]