Internal problem ID [3873]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 3
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _exact, _rational]
Solve \begin {gather*} \boxed {x +y y^{\prime }+\frac {x y^{\prime }}{x^{2}+y^{2}}-\frac {y}{x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 29
dsolve(x+y(x)*diff(y(x),x)+x/(x^2+y(x)^2)*diff(y(x),x)- y(x)/(x^2+y(x)^2)=0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\RootOf \left (-\left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x^{2}-x^{2}+2 c_{1}-2 \textit {\_Z} \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.12 (sec). Leaf size: 31
DSolve[x+y[x]*y'[x]+x/(x^2+y[x]^2)*y'[x]- y[x]/(x^2+y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\text {ArcTan}\left (\frac {x}{y(x)}\right )+\frac {x^2}{2}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]