76.1.18 problem 18

Internal problem ID [17317]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 09:59:51 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*}

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 17

dsolve([diff(y(x),x)=2*x/(1+2*y(x)),y(2) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 22

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

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