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labwork [276]
3 years ago
9

SOLVE. y''+3y'+2y=4e^x

Mathematics
1 answer:
olga55 [171]3 years ago
8 0
This a second order linear differential equation with the solution given by the general solution + the particular solution.
The general solution is given by Ae^mx + Be^nx; where m and n are solutions to the quadratic equation t^2 + 3t + 2 = 0
(t + 1)(t + 2) = 0
t = -1 or t = -2
general solution = Ae^(-x) + Be^(-2x)
For the particular solution, Ce^x + 3Ce^x + 2Ce^x = 4e^x
6Ce^x = 4e^x
C = 4/6 = 2/3

Therefore, solution is y = Ae^(-x) + Be^(-2x) + 2/3e^x
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Answer:

3x−4y=9 −3x+2y=9

Add these equations to eliminate x: −2y=18

Then solve−2y=18

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y=−9

Now that we've found y let's plug it back in to solve for x.

Write down an original equation: 3x−4y=9

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Answer: x=−9 and y=−9

Hope This Helps!!!

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Answer:

y = -2/3x + 4

Step-by-step explanation:

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The number with which "x" is multiplied is the slope.

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The y-intercept is 4, so it is the number with which no variable is multiplied.

So the equation is:

=> y = -2/3x + 4

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