Internal problem ID [38]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y y^{\prime }-x \left (1+y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
dsolve(y(x)*diff(y(x),x) = x*(1+y(x)^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{x^{2}} c_{1}-1} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{x^{2}} c_{1}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.317 (sec). Leaf size: 57
DSolve[y[x]*y'[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*}