7.3.12 problem 12

Internal problem ID [52]
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 1.4 (separable equations). Problems at page 43
Problem number : 12
Date solved : Friday, February 07, 2025 at 07:47:01 AM
CAS classification : [_separable]

\begin{align*} y y^{\prime }&=x \left (1+y^{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(y(x)*diff(y(x),x)=x*(y(x)^2+1),y(x), singsol=all)
 

\begin{align*} y &= \sqrt {c_1 \,{\mathrm e}^{x^{2}}-1} \\ y &= -\sqrt {c_1 \,{\mathrm e}^{x^{2}}-1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.987 (sec). Leaf size: 57

DSolve[y[x]*D[y[x],x]==x*(y[x]^2+1),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-1+e^{x^2+2 c_1}} \\ y(x)\to \sqrt {-1+e^{x^2+2 c_1}} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}