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3 years ago

14

What is the value of x in the equation

1 answer:

Nastasia [14]3 years ago

8 0

Answer:

54

Step-by-step explanation:

$\frac{1}{3x} - \frac{1}{2} = 18 \frac{1}{2} \\ \\ \frac{1}{3x} - \frac{1}{2} = \frac{37}{2} \\ \\ \frac{1}{3x} = \frac{37}{2} - \frac{1}{2} \\ \\ \frac{1}{3x} = \frac{37 - 1}{2} \\ \\ \frac{1}{3x} = \frac{36}{2} \\ \\ \frac{1}{3x} = 18 \\ \\ 1 = 54x$

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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

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I'll assume the ODE is

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Solve the homogeneous ODE,

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The characteristic equation

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has roots at $r=1$ and $r=2$ . Then the characteristic solution is

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For nonhomogeneous ODE (1),

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consider the ansatz particular solution

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Substituting this into (1) gives

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For the nonhomogeneous ODE (2),

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take the ansatz

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Substitute (2) into the ODE to get

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Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

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Klio2033 [76]

Answer:

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