Internal problem ID [8358]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 780.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }-\frac {y x +y+x \sqrt {y^{2}+x^{2}}}{x \left (x +1\right )}=0} \]
✓ Solution by Maple
Time used: 0.485 (sec). Leaf size: 27
dsolve(diff(y(x),x) = (x*y(x)+y(x)+x*(y(x)^2+x^2)^(1/2))/x/(x+1),y(x), singsol=all)
\[ c_{1} +\frac {\sqrt {y \left (x \right )^{2}+x^{2}}+y \left (x \right )}{x \left (x +1\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.46 (sec). Leaf size: 34
DSolve[y'[x] == (y[x] + x*y[x] + x*Sqrt[x^2 + y[x]^2])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{c_1} x (x+1)-\frac {e^{-c_1} x}{2 (x+1)} \\ \end{align*}