Question

Resolva a equação diferencial:
ydx+3xdy=0

Answer 1

y dx= -3x dy

-1/3x dx  = 1/y dy

- ∫ 1/3x dx  = ∫ 1/y dy

fazendo u=3x  ==>du=3dx

-∫1/u du/3 = ∫ 1/y dy

(-1/3) * ln u =  ln y + c

Como u =3x

(-1/3) * ln 3x + c= lny

y = e^( (-1/3) * ln 3x + c)

y = e^( (- ln ∛3x + c)

y=e^c * e^( (- ln ∛3x )    ....e^c=c₁

y=c₁ * e^( (- ln ∛3x ) 

Answer 2

Caso esteja pelo app, e tenha problemas para visualizar esta resposta, experimente abrir pelo navegador https://brainly.com.br/tarefa/13171271

                                               

$\sf y~dx+3x~dy=0\\\sf 3x~dy=-y~dx\\\sf\dfrac{dy}{y}=-\dfrac{dx}{3x}\\\displaystyle\sf\int\dfrac{dy}{y}=-\dfrac{1}{3}\int\dfrac{dx}{x}\\\sf \ell n|y|=-\dfrac{1}{3}\ell n|x|+c\\\sf e^{\ell n(y)}=e^{-\frac{1}{3}\ell n(x)+c}\\\sf e^{\ell n (y)}= e^{\ell n(x)^{-\frac{1}{3}}}\cdot e^c \\\sf y(x)=\dfrac{1}{\sqrt[\sf 3]{\sf x}}\cdot k\\\huge\boxed{\boxed{\boxed{\boxed{\sf y=\dfrac{k}{\sqrt[\sf3]{\sf x}}}}}}$