Internal problem ID [7810]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 230.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {a y y^{\prime }+b y^{2}+f \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 104
dsolve(a*y(x)*diff(y(x),x)+b*y(x)^2+f(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {{\mathrm e}^{-\frac {2 b x}{a}} \sqrt {-{\mathrm e}^{\frac {2 b x}{a}} a \left (-c_{1} a +2 \left (\int {\mathrm e}^{\frac {2 b x}{a}} f \relax (x )d x \right )\right )}}{a} \\ y \relax (x ) = -\frac {{\mathrm e}^{-\frac {2 b x}{a}} \sqrt {-{\mathrm e}^{\frac {2 b x}{a}} a \left (-c_{1} a +2 \left (\int {\mathrm e}^{\frac {2 b x}{a}} f \relax (x )d x \right )\right )}}{a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.344 (sec). Leaf size: 98
DSolve[a*y[x]*y'[x]+b*y[x]^2+f[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{-\frac {b x}{a}} \sqrt {2 \int _1^x-\frac {e^{\frac {2 b K[1]}{a}} f(K[1])}{a}dK[1]+c_1} \\ y(x)\to e^{-\frac {b x}{a}} \sqrt {2 \int _1^x-\frac {e^{\frac {2 b K[1]}{a}} f(K[1])}{a}dK[1]+c_1} \\ \end{align*}