Internal problem ID [9019]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 684.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }-\frac {y+x^{2} \sqrt {x^{2}+y^{2}}}{x}=0} \]
✓ Solution by Maple
Time used: 0.703 (sec). Leaf size: 30
dsolve(diff(y(x),x) = (y(x)+(y(x)^2+x^2)^(1/2)*x^2)/x,y(x), singsol=all)
\[ \ln \left (\sqrt {y \left (x \right )^{2}+x^{2}}+y \left (x \right )\right )-\frac {x^{2}}{2}-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.309 (sec). Leaf size: 36
DSolve[y'[x] == (y[x] + x^2*Sqrt[x^2 + y[x]^2])/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x e^{-\frac {x^2}{2}-c_1} \left (-1+e^{x^2+2 c_1}\right ) \]