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

For example, you have entered (calculator here):

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

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

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