10.2.14 problem 14

Internal problem ID [1142]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 14
Date solved : Saturday, March 29, 2025 at 10:41:19 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.069 (sec). Leaf size: 17

ode:=diff(y(x),x) = x*y(x)^2/(x^2+1)^(1/2); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.181 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.206 (sec). Leaf size: 15

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

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