Internal problem ID [945]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x}{1+2 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 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)
\[ y \relax (x ) = -\frac {1}{2}+\frac {\sqrt {4 x^{2}-15}}{2} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 22
DSolve[{y'[x]==2*x/(1+2*y[x]),y[2]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\sqrt {4 x^2-15}-1\right ) \\ \end{align*}