31.2.4 problem 4

Internal problem ID [5725]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 4
Date solved : Monday, January 27, 2025 at 01:11:38 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact, _rational]

\begin{align*} x +y^{\prime } y+\frac {x y^{\prime }}{x^{2}+y^{2}}-\frac {y}{x^{2}+y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.171 (sec). Leaf size: 26

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)
 

\[ y \left (x \right ) = \cot \left (\operatorname {RootOf}\left (2 \sin \left (\textit {\_Z} \right )^{2} c_{1} -2 \textit {\_Z} \sin \left (\textit {\_Z} \right )^{2}+x^{2}\right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 31

DSolve[x+y[x]*D[y[x],x]+x/(x^2+y[x]^2)*D[y[x],x]- y[x]/(x^2+y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\arctan \left (\frac {x}{y(x)}\right )+\frac {x^2}{2}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]