- #1

Jhenrique

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## Homework Statement

Get the solution (for y(x)) for the follows integrals: [tex]\int y(x) dx = ky\;\;\;\;\;(1)[/tex] [tex]\int y(x) dx = \frac{k}{y}\;\;\;\;\;(2)[/tex] [tex]\int y(x) dx = kx\;\;\;\;\;(3)[/tex] [tex]\int y(x) dx = \frac{k}{x}\;\;\;\;\;(4)[/tex]

## Homework Equations

## The Attempt at a Solution

[tex]\\ \int y(x)dx = kx \\ \\ \int y(x)\frac{dx}{dx} = \frac{kx}{dx} \\ \\ d\int y(x) = d\frac{kx}{dx} \\ \\ y(x) = k\frac{dx}{dx} \\ \\ y(x) = k[/tex]

[tex]\\ \int y(x)dx = \frac{k}{x} \\ \\ \int y(x)\frac{dx}{dx} = \frac{1}{dx} \frac{k}{x} \\ \\ d\int y(x) = \frac{d}{dx} \frac{k}{x} \\ \\ y(x) = k \frac{d}{dx}\left ( \frac{1}{x} \right ) \\ \\ y(x) = -\frac{k}{x^2}[/tex]