Internal problem ID [8353]
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]
\[ \boxed {y^{\prime }+y^{2}+\left (y x -1\right ) f \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 75
dsolve(diff(y(x),x) + y(x)^2 +(x*y(x)-1)*f(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-\left (\int \frac {f \left (x \right ) x^{2}+2}{x}d x \right )} x +\int {\mathrm e}^{-\left (\int \frac {f \left (x \right ) x^{2}+2}{x}d x \right )}d x -c_{1}}{\left (-c_{1} +\int {\mathrm e}^{-\left (\int \frac {f \left (x \right ) x^{2}+2}{x}d x \right )}d x \right ) x} \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 114
DSolve[y'[x] + y[x]^2 +(x*y[x]-1)*f[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \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}{x \left (\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\right )} \\ y(x)\to \frac {1}{x} \\ \end{align*}