Juliianatafur22

16.12.2021 •

Mathematics

Are triangles ABC and ADC congruent? Yes, by SSS
Yes, by ASA
Yes, by SAS
Not enough information

Are triangles ABC and ADC congruent?

Yes, by SSS
Yes, by ASA
Yes, by SAS
Not enough information

Solved

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Ответ:

jelopez4

15.05.2023

Mathematics

$y_p(x) =c_1e^{-6x} + c_2e^{-3x}+ e^x + 4x^2$

Step-by-step explanation:

Given

y" + 9y' + 18y = 24x^2 + 40x + 8 + 12e^x ---- (1)

y_p(x) = e^x + 4x^2

Required

The general solution of y(x)

Let

$y = e^{nx}$ be the trial solution of (1)

So:

y" + 9y' + 18y = 0 becomes

n^2 + 9n + 18 = 0

Expand

n^2 + 6n+3n + 18 = 0

Factorize

n(n + 6)+3(n + 6) = 0

Factor out n + 6

(n + 6)(n + 3) = 0

Split

$n +6 = 0\ or\ n + 3 = 0$

Solve for n

$n =-6\ or\ n = -3$

So:

$y = e^{nx}$ becomes:

$y = c_1e^{-6x} + c_2e^{-3x}$

y_p(x) = e^x + 4x^2 becomes

$y_p(x) =c_1e^{-6x} + c_2e^{-3x}+ e^x + 4x^2$

Where: c_1 and c_2 are arbitary constants

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Are triangles ABC and ADC congruent? Yes, by SSS Yes, by ASA Yes, by SAS Not enough information