12.3.6 problem 7

Internal problem ID [1583]
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 : 7
Date solved : Monday, January 27, 2025 at 05:09:22 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: 0.175 (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*}