48.1.1 problem Example 3.1

Internal problem ID [7502]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page 114
Problem number : Example 3.1
Date solved : Monday, January 27, 2025 at 03:02:46 PM
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*(y(x)^2+1),y(x), singsol=all)
 

\[ y = \tan \left (\frac {x^{3}}{3}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.231 (sec). Leaf size: 30

DSolve[D[y[x],x]==x^2*(y[x]^2+1),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*}