# A simplest differential equations of 1-order Step-by-Step

$$x \frac{d}{d x} y{\left(x \right)} - 3 = 0$$

### Detail solution

Divide both sides of the equation by the multiplier of the derivative of y':$$x$$

We get the equation:

y' = $$\frac{3}{x}$$

This differential equation has the form:

y' = f(x)

It is solved by multiplying both sides of the equation by dx:

y'dx = f(x)dx, or

d(y) = f(x)dx

And by using the integrals of the both equation sides:

∫ d(y) = ∫ f(x) dx

or

y = ∫ f(x) dx

In this case,

f(x) = $$\frac{3}{x}$$

Consequently, the solution will be

y = $$\int \frac{3}{x}\, dx$$

or

y = $$3 \log{\left(x \right)}$$ + C1

where C1 is constant, independent of x