12.25 problem Ex 26

Internal problem ID [10181]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number: Ex 26.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {\left (y^{2}+x^{2}\right ) \left (x +y^{\prime } y\right )+\sqrt {1+x^{2}+y^{2}}\, \left (-y^{\prime } x +y\right )=0} \end {gather*}

Solution by Maple

Time used: 0.062 (sec). Leaf size: 27

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

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

Solution by Mathematica

Time used: 0.309 (sec). Leaf size: 27

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

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