Internal problem ID [7615]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+f \relax (x ) y^{2}+g \relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(y(x),x) + f(x)*y(x)^2 + g(x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{\int -g \relax (x )d x}}{\int {\mathrm e}^{\int -g \relax (x )d x} f \relax (x )d x +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.303 (sec). Leaf size: 59
DSolve[y'[x] + f[x]*y[x]^2 + g[x]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\exp \left (\int _1^x-g(K[1])dK[1]\right )}{-\int _1^x-\exp \left (\int _1^{K[2]}-g(K[1])dK[1]\right ) f(K[2])dK[2]+c_1} \\ y(x)\to 0 \\ \end{align*}