Internal problem ID [2098]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1-y^{2}}{2 y x +2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(y(x),x)=(1-y(x)^2)/(2*(1+x*y(x))),y(x), singsol=all)
\[ c_{1}+\frac {1}{\left (y \relax (x )-1\right ) \left (2+x \left (y \relax (x )+1\right )\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.424 (sec). Leaf size: 56
DSolve[y'[x]==(1-y[x]^2)/(2*(1+x*y[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1+\sqrt {1+x (x+c_1)}}{x} \\ y(x)\to \frac {-1+\sqrt {1+x (x+c_1)}}{x} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}