Internal problem ID [592]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {\frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.022 (sec). Leaf size: 19
dsolve(2*x/y(x)-y(x)/(x^2+y(x)^2)+(-x^2/y(x)^2+x/(x^2+y(x)^2))*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{\tan \left (\RootOf \left (-\textit {\_Z} +x \tan \left (\textit {\_Z} \right )+c_{1}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.288 (sec). Leaf size: 23
DSolve[2*x/y[x]-y[x]/(x^2+y[x]^2)+(-x^2/y[x]^2+x/(x^2+y[x]^2))*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {ArcTan}\left (\frac {x}{y(x)}\right )-\frac {x^2}{y(x)}=c_1,y(x)\right ] \]