77.1.35 problem 52 (page 96)

Internal problem ID [17925]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 52 (page 96)
Date solved : Tuesday, January 28, 2025 at 11:12:50 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact]

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

✓ Solution by Maple

Time used: 0.452 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.278 (sec). Leaf size: 27

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

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