Internal problem ID [2945]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 197.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {y^{\prime } x -y+x \left (x -y\right ) \sqrt {x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 49
dsolve(x*diff(y(x),x) = y(x)-x*(x-y(x))*sqrt(x^2+y(x)^2),y(x), singsol=all)
\[ \ln \left (\frac {2 x \left (\sqrt {2 x^{2}+2 y \relax (x )^{2}}+y \relax (x )+x \right )}{-x +y \relax (x )}\right )+\frac {\sqrt {2}\, x^{2}}{2}-\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.378 (sec). Leaf size: 71
DSolve[x y'[x]==y[x]-x(x-y[x])Sqrt[x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x \left (\sqrt {2} \tanh \left (\frac {x^2+2 c_1}{2 \sqrt {2}}\right )-\frac {1}{1+\sqrt {2} \tanh \left (\frac {x^2+2 c_1}{2 \sqrt {2}}\right )}+1\right ) \\ y(x)\to x \\ \end{align*}