12.1.5 problem 2(e)

Internal problem ID [1523]
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 : 2(e)
Date solved : Monday, January 27, 2025 at 04:58:50 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

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

\[ y = \tan \left (\frac {x^{3}}{3}+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 30

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

\begin{align*} y(x)\to \tan \left (\frac {x^3}{3}+c_1\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}