Find the general solution for the differential equation dy+7xdx=0 and the particular solution if y(0)=3?

First, we'll have to isolate dy to the left side. For this
reason, we'll subtract 7x dx both sides:

dy = -7x
dx

Now, we'll integrate both
sides:

`int` dy = `int` -7x
dx

y = -7x^2/2 + C

The general
solution of the differential equation is y = -7x^2/2 + C. To find the particular
solution of the differential equation, we'll have to determine the constant C. We'll use
the information provided by enunciation y(0) = 3.

That
means that if x =0 => y = -7*0^2/2 + C = 3

C =
3

The particular solution of the differential equation is
the quadratic y = -7x^2/2 + 3.

Therefore, the
general solution of the differential equation is y = -7x^2/2 + C and the particular
solution of the differential equation is the quadratic y = -7x^2/2 +
3.