31.2.8 problem 8.1

Internal problem ID [5729]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 8.1
Date solved : Monday, January 27, 2025 at 01:11:41 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact]

\begin{align*} \frac {x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.147 (sec). Leaf size: 25

dsolve( x/sqrt(1+x^2+y(x)^2) + y(x)/sqrt(1+x^2+y(x)^2)*diff(y(x),x)+  y(x)/(x^2+y(x)^2) - x/(x^2+y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.287 (sec). Leaf size: 27

DSolve[ x/Sqrt[1+x^2+y[x]^2] + y[x]/Sqrt[1+x^2+y[x]^2]*D[y[x],x]+y[x]/(x^2+y[x]^2) - x/(x^2+y[x]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\arctan \left (\frac {x}{y(x)}\right )+\sqrt {x^2+y(x)^2+1}=c_1,y(x)\right ] \]