12.3.15 problem 16

Internal problem ID [1592]
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 : 16
Date solved : Monday, January 27, 2025 at 05:12:36 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 x y \left (1+y^{2}\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 16

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

\[ y = \frac {1}{\sqrt {2 \,{\mathrm e}^{-2 x^{2}}-1}} \]

✓ Solution by Mathematica

Time used: 60.090 (sec). Leaf size: 27

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

\[ y(x)\to \frac {i e^{x^2}}{\sqrt {e^{2 x^2}-2}} \]