Example
Consider the Bernoulli equation
We first notice that is a solution. Division by yields
Changing variables gives the equations
which can be solved using the integrating factor
Multiplying by ,
Note that left side is the derivative of . Integrating both sides results in the equations
The solution for is
as well as .
Verifying using MATLAB symbolic toolbox by running
x = dsolve('Dy-2*y/x=-x^2*y^2','x')gives both solutions:
0 x^2/(x^5/5 + C1)also see a solution by WolframAlpha, where the trivial solution is missing.
Read more about this topic: Bernoulli Differential Equation
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—Marcel Proust (1871–1922)