12.1.14 problem 5(c)

Internal problem ID [1532]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 5(c)
Date solved : Monday, January 27, 2025 at 04:59:03 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 10

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

\[ y = \tan \left (\frac {x^{2}}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.179 (sec). Leaf size: 13

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

\[ y(x)\to \tan \left (\frac {x^2}{2}\right ) \]