Question

calcule equações diferenciais de x dy/dx = y

Answer 1

 x dy/dx = y

(1/y) dy = (1/x) dx

∫(1/y) dy = ∫(1/x) dx

ln y = ln x + c₁   ...c₁ é uma constante ..fazendo c₁=ln c₂

ln y = ln x + ln c₂

y=c₂ *x

Answer 2

Resposta:

$\boxed{\mathtt{y = Cx}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{x \ \frac{dy}{dx} = y} \\\\\\ \mathsf{\frac{dy}{dx} = \frac{y}{x}} \\\\\\ \mathsf{\frac{dy}{y} = \frac{dx}{x}} \\\\\\ \mathsf{\int \frac{1}{y} \ dy = \int \frac{1}{x} \ dx} \\\\\\ \mathsf{\int \frac{1}{y} \ dy = \int \frac{1}{x} \ dx} \\\\ \mathsf{\ln |y| = \ln |x| + c} \\\\ \mathsf{\ln |y| - \ln |x| = c} \\\\ \mathsf{\ln \frac{|y|}{|x|} = c} \\\\ \mathsf{e^c = \frac{y}{x}, \qquad \qquad 0 < y < \infty} \\\\ \boxed{\boxed{\mathsf{y = Cx}}}$