Question

Preciso da Resolução da função y que satisfaz a equação diferencial
$\frac{dx}{dy} = x-6$

Answer 1

$\displaystyle\int x^{n}dx=\frac{x^{n+1}}{n+1}~~~se~n\neq-1$
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$\dfrac{dy}{dx}=x-6~~~~\therefore~~~~\boxed{\boxed{dy=(x-6)dx}}$

y será dada pela integral de dy, logo:

$y=\displaystyle\int dy\\\\\\y=\int(x-6)dx\\\\\\y=\int x^{1}dx-\int6x^{0}dx\\\\\\y=\dfrac{x^{1+1}}{1+1}-6\dfrac{x^{0+1}}{0+1}+constante\\\\\\\boxed{\boxed{y=\dfrac{x^{2}}{2}-6x+constante}}$