Internal problem ID [2944]
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)]]]
Solve \begin {gather*} \boxed {y^{\prime } x -y-x \sqrt {x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.418 (sec). Leaf size: 28
dsolve(x*diff(y(x),x) = y(x)+x*sqrt(x^2+y(x)^2),y(x), singsol=all)
\[ \ln \left (y \relax (x )+\sqrt {x^{2}+y \relax (x )^{2}}\right )-x -\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 44.714 (sec). Leaf size: 46
DSolve[x y'[x]==y[x]+x Sqrt[x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x \tanh (x+c_1)}{\sqrt {\text {sech}^2(x+c_1)}} \\ y(x)\to \frac {x \tanh (x+c_1)}{\sqrt {\text {sech}^2(x+c_1)}} \\ \end{align*}