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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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.

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