Internal problem ID [9325]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 991.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _Riccati]
\[ \boxed {y^{\prime }+F \left (x \right ) \left (x^{2}+2 x y-y^{2}\right )-\frac {y}{x}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 29
dsolve(diff(y(x),x) = -F(x)*(x^2+2*x*y(x)-y(x)^2)+y(x)/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \left (\sqrt {2}-2 \tanh \left (\left (\int F \left (x \right ) x d x +c_{1} \right ) \sqrt {2}\right )\right ) \sqrt {2}}{2} \]
✓ Solution by Mathematica
Time used: 0.56 (sec). Leaf size: 104
DSolve[y'[x] == y[x]/x - F[x]*(x^2 + 2*x*y[x] - y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \left (-\left (\sqrt {2}-1\right ) \exp \left (2 \sqrt {2} \left (\int _1^xF(K[1]) K[1]dK[1]+c_1\right )\right )+1+\sqrt {2}\right )}{1+\exp \left (2 \sqrt {2} \left (\int _1^xF(K[1]) K[1]dK[1]+c_1\right )\right )} \\ y(x)\to \left (1+\sqrt {2}\right ) x \\ y(x)\to x-\sqrt {2} x \\ \end{align*}