8.3.12 problem 12

Internal problem ID [688]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 12
Date solved : Wednesday, February 05, 2025 at 03:51:10 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*(1+y(x)^2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 6.923 (sec). Leaf size: 57

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