10.2.15 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 : Monday, January 27, 2025 at 04:35:39 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: 0.361 (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: 0.104 (sec). Leaf size: 22

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

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