Mister Exam

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

For example, you have entered (calculator here):
$$x \frac{d}{d x} y{\left(x \right)} - 3 = 0$$

### 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 = $$\int \frac{3}{x}\, dx$$
Detailed solution of the integral
or
y = $$3 \log{\left(x \right)}$$ + C1
where C1 is constant, independent of x