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3 years ago

Please please help me!!!!!!!

Mathematics

1 answer:

Jlenok [28]3 years ago

7 0

Answer:

Step-by-step explanation:

Hope this helps! Good luck!

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Use the method of "undetermined coefficients" to find a particular solution of the differential equation. (The solution found ma

Naddika [18.5K]

Answer:

The particular solution of the differential equation

= $\frac{-1,36,656cos5x+1,89,800 sin5x}{-1204}$ + $\frac{1}{37}185e^{6x})$

Step-by-step explanation:

Given differential equation y''(x) − 10y'(x) + 61y(x) = −3796 cos(5x) + 185e6x

The differential operator form $(D^{2} -10D+61)y(x) = −3796 cos(5x) + 185e^{6x}$

<u>Rules for finding particular integral in some special cases:-</u>

let f(D)y = $e^{ax}$ then

the particular integral $\frac{1}{f(D)} (e^{ax} ) = \frac{1}{f(a)} (e^{ax} ) if f(a)$ ≠ 0

let f(D)y = cos (ax ) then

the particular integral $\frac{1}{f(D)} (cosax ) = \frac{1}{f(D^2)} (cosax ) =\frac{cosax}{f(-a^2)}$ f(-a^2) ≠ 0

Given problem

$(D^{2} -10D+61)y(x) = −3796 cos(5x) + 185e^{6x}$

P<u>articular integral</u>:-

$P.I = \frac{1}{f(D)}( −3796 cos(5x) + 185e^{6x})$

$P.I = \frac{1}{D^2-10D+61}( −3796 cos(5x) + 185e^{6x})$

$P.I = \frac{1}{D^2-10D+61}( −3796 cos(5x) + \frac{1}{D^2-10D+61}185e^{6x})$

P.I = $I_{1} +I_{2}$

we will apply above two conditions, we get

$I_{1}$ =

$\frac{1}{D^2-10D+61}( −3796 cos(5x) = \frac{1}{(-25)-10D+61}( −3796 cos(5x) ( since D^2 = - 5^2)$ $= \frac{1}{(36-10D}( −3796 cos(5x) \\= \frac{1}{(36-10D}X\frac{36+10D}{36+10D} ( −3796 cos(5x)$

on simplification we get

= $\frac{1}{(36^2-(10D)^2}36+10D( −3796 cos(5x)$

= $\frac{-1,36,656cos5x+1,89,800 sin5x}{1296-100(-25)}$

= $\frac{-1,36,656cos5x+1,89,800 sin5x}{-1204}$

$I_{2}$ =

$\frac{1}{D^2-10D+61}185e^{6x}) = \frac{1}{6^2-10(6)+61}185e^{6x})$

$\frac{1}{37}185e^{6x})$

Now particular solution

P.I = $I_{1} +I_{2}$

P.I = $\frac{-1,36,656cos5x+1,89,800 sin5x}{-1204}$ + $\frac{1}{37}185e^{6x})$

8 0

3 years ago

Plssssss help due today

Grace [21]

10^2 - 8^2
= 100 - 64
= 36
LM = √36 = 6

answer
LM = 6

8 0

3 years ago

if i have the amount of 182 and i minus $8.00 and $4.30 and i get 172.37 dollars how many do i have left

Blababa [14]

By “i get 172.37” is that adding to the 182 or how much you have left after buying those things.

3 0

3 years ago

The area of a trapezium is 800 cm2

svlad2 [7]

Answer:

The distance between the parallel sides is 20cm.

Step-by-step explanation:

Area of a trapezoid:

$A=\frac{a+b}{2}\times h$

where a and b are the 2 bases, and h is the height. The value we're trying to find here is the height.

3 of the 4 variables in this equation are already given:

A = 800

a = 48

b = 32

Just plug those in and solve for h:

$\rightarrow 800=\frac{48+32}{2}\times h\\\rightarrow 800=\frac{80}{2}\times h\\\rightarrow 800=40\times h\\\rightarrow 800\div40=h\\\rightarrow h=20$

5 0

3 years ago

Read 2 more answers

Find the area of each figure

seraphim [82]

3 times 3 times 3 times 3 equals 81 so it would be 81

7 0

3 years ago