Question

solve the differential equation

Answer 1

\[\frac{ dy }{ dx }= \frac{ y^2+xy+x^2 }{ x^2 }\]

Answer 2

@Zepdrix

Answer 3

1st order homogeneous' \(\)

use the sub: \(v = \dfrac{y}{x}\) and \(y' = v'x + v\)

then separate

Answer 4

oh , how come we aint using bernoulli?

Answer 5

1st order Homo's tend to stand out a bit and they're often pretty tame

Bernoulli is more work, so comes further down the list of "what should i do?"

Plus the Bernoulli form is: \(y' + Py = Q y^{n}\)

whereas here you have:

\(y' - \frac{1}{x} y = \frac{y^2}{x^2} + 1\)