7.2.9 problem 11

Internal problem ID [27]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.3. Problems at page 27
Problem number : 11
Date solved : Friday, February 07, 2025 at 08:12:08 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.157 (sec). Leaf size: 16

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

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