Internal problem ID [3452]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 196.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime } x -y-x \sqrt {x^{2}+y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.437 (sec). Leaf size: 28
dsolve(x*diff(y(x),x) = y(x)+x*sqrt(x^2+y(x)^2),y(x), singsol=all)
\[ \ln \left (y \left (x \right )+\sqrt {x^{2}+y \left (x \right )^{2}}\right )-x -\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.282 (sec). Leaf size: 30
DSolve[x y'[x]==y[x]+x Sqrt[x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x e^{-x-c_1} \left (-1+e^{2 (x+c_1)}\right ) \]