Internal problem ID [493]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 15.
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: 0.022 (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: 0.085 (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*}