How do you solve separable first-order differential equations?

wadiad6qxb

wadiad6qxb

Answered question

2022-04-11

How do you solve separable first-order differential equations?

Answer & Explanation

firyemv3

firyemv3

Beginner2022-04-12Added 10 answers

A separable equation typically looks like:
dydx=g(x)f(y)
By multiplying by dx and by g(y) to separate x's and y's,
f(y)dy=g(x)dx
By integrating both sides,
f(y)dy=g(x)dx,
which gives us the solution expressed implicitly:
F(y)=G(x)+C,
where F and G are antiderivatives of f and g, respectively.
zvonkurm7h

zvonkurm7h

Beginner2022-04-13Added 8 answers

A first-order differential equation is said to be separable if, after solving it for the derivative, dy dx = F(x, y) , the right-hand side can then be factored as "a formula of just x " times "a formula of just y ", F(x, y) = f (x)g(y).

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