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3 years ago

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Can someone pls pls pls answer this!??

2 answers:

Tom [10]3 years ago

5 0

I cant see it bro take another picture and i can help

Zina [86]3 years ago

3 0

I can’t see it sry buddy :((

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Consider the following differential equation to be solved by undetermined coefficients. y(4) − 2y''' + y'' = ex + 1 Write the gi

kompoz [17]

Answer:

The general solution is

$y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

+ $\frac{x^2}{2}$

Step-by-step explanation:

Step :1:-

Given differential equation y(4) − 2y''' + y'' = e^x + 1

The differential operator form of the given differential equation

$(D^4 -2D^3+D^2)y = e^x+1$

comparing f(D)y = e^ x+1

The auxiliary equation (A.E) f(m) = 0

$m^4 -2m^3+m^2 = 0$

$m^2(m^2 -2m+1) = 0$

$(m^2 -2m+1) this is the expansion of (a-b)^2$

$m^2 =0 and (m-1)^2 =0$

The roots are m=0,0 and m =1,1

complementary function is $y_{c} = (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x$

<u>Step 2</u>:-

The particular equation is $\frac{1}{f(D)} Q$

P.I = $\frac{1}{D^2(D-1)^2} e^x+1$

P.I = $\frac{1}{D^2(D-1)^2} e^x+\frac{1}{D^2(D-1)^2}e^{0x}$

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

$\frac{1}{D^2} (\frac{x^2}{2!} )e^x + \frac{1}{D^{2} } e^{0x}$

$\frac{1}{D} means integration$

$\frac{1}{D^2} (\frac{x^2}{2!} )e^x = \frac{1}{2D} \int\limits {x^2e^x} \, dx$

applying in integration u v formula

$\int\limits {uv} \, dx = u\int\limits {v} \, dx - \int\limits ({u^{l}\int\limits{v} \, dx } )\, dx$

$I_{1}$ = $\frac{1}{D^2(D-1)^2} e^x$

$\frac{1}{2D} (e^x(x^2)-e^x(2x)+e^x(2))$

$\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

$I_{2}$ $= \frac{1}{D^2(D-1)^2}e^{0x}$

$\frac{1}{D} \int\limits {1} \, dx= \frac{1}{D} x$

again integration $\frac{1}{D} x = \frac{x^2}{2!}$

The general solution is $y = y_{C} +y_{P}$

$y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

+ $\frac{x^2}{2!}$

3 0

3 years ago

NEED HELP ASAP!!

BARSIC [14]

84 square inches divided by 14 inches equals 6

84 divided by 14 = s

7 0

3 years ago

Read 2 more answers

the length of a rectangle is 5ft longer than it's width. if the perimeter of the rectangle is 34ft, find it's area?

galina1969 [7]

2X + (2X+10)= 34

Width is 6, Length is 11

6 x 11 is 66

Area is 66

7 0

3 years ago

SOLVE FOR BRAINLIEST!

marissa [1.9K]

I think it would be the second question!

7 0

2 years ago

From a height of 50 meters above sea level on a cliff, two ships are sighted due west. The angles of depression are 61° and 28°.

Olenka [21]

Answer:

The ships are 66 meters apart.

Step-by-step explanation:

For the sake of convenience, let us label ships A and B

As shown in the figure, the distances to the ships from right triangles.

The distance to the ship A is $d_1$ and it is given by

$tan (61^o)= \dfrac{50}{d_1}$

$d_1=\dfrac{50}{tan (61^o)}$

$\boxed{d_1= 27.71m}$

And the distance to the ship B is $d_2$ and is given by

$tan (28^o)= \dfrac{50}{d_2}$

$d_2=\dfrac{50}{tan (28^o)}$

$\boxed{ d_2=94.04m}$

Therefore, the distance $d$ between the ships A and B is

$d= d_2-d_1=94.04-27.7\\\\\boxed{d=66m}$

In other words, the ships are 66 meters apart.

8 0

3 years ago

Read 2 more answers