13.1.6 problem 6

Internal problem ID [3520]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 06:41:10 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2 x \left (y-1\right )}{x^{2}+3} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(y(x),x) = 2*x*(y(x)-1)/(x^2+3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{2}+3 c_1 +1 \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 20

ode=D[y[x],x]==(2*x*(y[x]-1))/(x^2+3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 1+c_1 \left (x^2+3\right )\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.148 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*(y(x) - 1)/(x**2 + 3) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{2} + 3 C_{1} + 1 \]