4.2.15 problem 15

Internal problem ID [1143]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 04:23:42 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.084 (sec). Leaf size: 17

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

\[ y = -\frac {1}{2}+\frac {\sqrt {4 x^{2}-15}}{2} \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \frac {1}{2} \left (\sqrt {4 x^2-15}-1\right ) \end{align*}

✓ Sympy. Time used: 0.275 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {\sqrt {4 x^{2} - 15}}{2} - \frac {1}{2} \]