Internal problem ID [7809]
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]
\[ \boxed {a y y^{\prime }+b y^{2}+f \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) = \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 \left (x \right )d x \right )\right )}}{a} \\ y \left (x \right ) = -\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 \left (x \right )d x \right )\right )}}{a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.349 (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*}