12.3.18 problem 19

Internal problem ID [1595]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 19
Date solved : Monday, January 27, 2025 at 05:12:53 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: 0.016 (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: 0.105 (sec). Leaf size: 22

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

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