50.2.15 problem 2(e)

Internal problem ID [7821]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 2(e)
Date solved : Monday, January 27, 2025 at 03:24:12 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x^{2} y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 15

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

\[ y = -\frac {6}{2 x^{3}-1} \]

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 16

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

\[ y(x)\to \frac {6}{1-2 x^3} \]