10.2.13 problem 13

Internal problem ID [1141]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 13
Date solved : Tuesday, March 04, 2025 at 12:11:16 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=-2 \end{align*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 18

ode:=diff(y(x),x) = 2*x/(y(x)+x^2*y(x)); 
ic:=y(0) = -2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\sqrt {2 \ln \left (x^{2}+1\right )+4} \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 24

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

\[ y(x)\to -\sqrt {2} \sqrt {\log \left (x^2+1\right )+2} \]

✓ Sympy. Time used: 0.470 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = - \sqrt {2 \log {\left (x^{2} + 1 \right )} + 4} \]