7.5.64 problem 65

Internal problem ID [168]
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 1.6 (substitution and exact equations). Problems at page 72
Problem number : 65
Date solved : Saturday, March 29, 2025 at 04:37:59 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

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

\[ y = \frac {c_1 x +x^{2}-1}{x +c_1} \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.242 (sec). Leaf size: 14

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

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