Find the particular solution of the differential equation dy + 7y = 6 satisfying the initial condition y(0) = 0. y= your answer should be a function of x.

Step-by-step explanation:

We have the equation with the initial condition . It is not difficult to notice that this is a linear equation, which has the general expression

.

The solution of this equation is expressed by a general formula:

.

In the particular case of our equation, we have

.

Then, we must calculate the integrals

that implies

,

and

Then,

.

In order to obtain the value of the constant we substitute the initial condition

that implies

Therefore,

.

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step-by-step explanation: