20.1.21 problem Problem 29

Internal problem ID [3578]
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
Date solved : Monday, January 27, 2025 at 07:45:27 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {1-y^{2}}{2+2 y x} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 21

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

\[ c_{1} +\frac {1}{\left (y \left (x \right )-1\right ) \left (x y \left (x \right )+x +2\right )} = 0 \]

✓ Solution by Mathematica

Time used: 0.429 (sec). Leaf size: 58

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

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