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3 years ago

Can somebody help me? and explain how to do this?

Mathematics

1 answer:

disa [49]3 years ago

8 0

Answer:

The correct answer is last option

2n + m√n - nm

Step-by-step explanation:

It is given an expression,

4√n² + √m²n - √4n² - √mn²

<u>To simplify the expression</u>

4√n² + √m²n - √4n² - √mn² = 4n + m√n -2n -nm

= 4n - 2n + m√n - n√m

= 2n + m√n - n√m

Therefore the correct answer is last option

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Answer:

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B) Homogeneous solution:

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C) The most general solution is

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Step-by-step explanation:

Given non homogeneous ODE is

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$D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)$

To find particular solution:

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Substituting $y_{p},y'_{p},y''_{p}$ in (1)

$y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\$

Equating the coefficients

$5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\$

The general solution is

$y=y_{h}+y_{p}$

from (2) ad (3)

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