Internal problem ID [7597]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+y^{2}+\left (y x -1\right ) f \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 50
dsolve(diff(y(x),x) + y(x)^2 +(x*y(x)-1)*f(x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{\int -\frac {f \relax (x ) x^{2}+2}{x}d x}}{c_{1}-\left (\int {\mathrm e}^{\int -\frac {f \relax (x ) x^{2}+2}{x}d x}d x \right )}+\frac {1}{x} \]
✓ Solution by Mathematica
Time used: 0.277 (sec). Leaf size: 78
DSolve[y'[x] + y[x]^2 +(x*y[x]-1)*f[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x}+\frac {\exp \left (-\int _1^x\left (f(K[1]) K[1]+\frac {2}{K[1]}\right )dK[1]\right )}{\int _1^x\exp \left (-\int _1^{K[2]}\left (f(K[1]) K[1]+\frac {2}{K[1]}\right )dK[1]\right )dK[2]+c_1} \\ y(x)\to \frac {1}{x} \\ \end{align*}