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Solve the given differential equations.$$d y+3 y d x=e^{-3 x} d x$$

$\frac{x}{e^{3 x}}+\frac{c}{e^{3 x}}$

Calculus 2 / BC

Chapter 31

Differential Equations

Section 4

The Linear Differential Equation of the First Order

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Solve the differential equ…

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Solve the given differenti…

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For the following problems…

we want to solve this differential equation here. So notice first, This is a separable equation because if we multiply each side by eat the wind, he can't sell it on the right and on the left will have e to the wife Times do I buy D X is equal to three x squared Now let's go ahead and multiply O r dx over and I say multiply. It won't. It's because we can't really multiply by t x Uh, but now we're going to integrate each side. Now the inter grody to the why should just be eat. Why the integral of three ex cute Well, that's gonna be power also should be excused and then we divide by three So the threes cancel and then we have our constant C. Now we just need to take natural log on each side so we can get why by itself. So why is going to be natural? Aga X Cube? We'll see. So this here will be our solution to this differential equation

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