Internal problem ID [3450]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 194.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x y^{\prime }-y-\sqrt {y^{2}+x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(x*diff(y(x),x) = y(x)+sqrt(x^2+y(x)^2),y(x), singsol=all)
\[ \frac {-c_{1} x^{2}+\sqrt {x^{2}+y \left (x \right )^{2}}+y \left (x \right )}{x^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.352 (sec). Leaf size: 27
DSolve[x y'[x]==y[x]+Sqrt[x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-c_1} \left (-1+e^{2 c_1} x^2\right ) \]