Internal problem ID [5400]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2} x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 15
dsolve([diff(y(x),x)=x^2*y(x)^2,y(-1) = 2],y(x), singsol=all)
\[ y \relax (x ) = -\frac {6}{2 x^{3}-1} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 16
DSolve[{y'[x]==x^2*y[x]^2,{y[-1]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {6}{1-2 x^3} \\ \end{align*}