Internal problem ID [3453]
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)]`]]
\[ \boxed {y^{\prime } x -y+x \left (-y+x \right ) \sqrt {x^{2}+y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.047 (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)
\[ \ln \left (\frac {2 x \left (\sqrt {2 x^{2}+2 y \left (x \right )^{2}}+y \left (x \right )+x \right )}{y \left (x \right )-x}\right )+\frac {\sqrt {2}\, x^{2}}{2}-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.529 (sec). Leaf size: 84
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 {x \tanh \left (\frac {x^2+2 c_1}{2 \sqrt {2}}\right ) \left (2+\sqrt {2} \tanh \left (\frac {x^2+2 c_1}{2 \sqrt {2}}\right )\right )}{\sqrt {2}+2 \tanh \left (\frac {x^2+2 c_1}{2 \sqrt {2}}\right )} y(x)\to x \end{align*}