Internal problem ID [5243]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _dAlembert]
\[ \boxed {y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 51
dsolve(y(x)*sqrt(x^2+y(x)^2)-x*(x+sqrt(x^2+y(x)^2))*diff(y(x),x)=0,y(x), singsol=all)
\[ \ln \left (\frac {2 x \left (x +\sqrt {x^{2}+y^{2}}\right )}{y}\right )-\ln \left (y\right )-\frac {\sqrt {x^{2}+y^{2}}}{x}-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.319 (sec). Leaf size: 43
DSolve[y[x]*Sqrt[x^2+y[x]^2]-x*(x+Sqrt[x^2+y[x]^2])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\sqrt {\frac {y(x)^2}{x^2}+1}+\log \left (\sqrt {\frac {y(x)^2}{x^2}+1}-1\right )=-\log (x)+c_1,y(x)\right ] \]