Internal problem ID [2211]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page
91
Problem number: Problem 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, _Riccati]
Solve \begin {gather*} \boxed {\frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 12
dsolve((1/x-y(x)/(x^2+y(x)^2))+x/(x^2+y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\tan \left (\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.188 (sec). Leaf size: 15
DSolve[(1/x-y[x]/(x^2+y[x]^2))+x/(x^2+y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan (-\log (x)+c_1) \\ \end{align*}