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3 years ago

If EF equals 2X -12, FG equals 3X -15 and e.g. equals 23 find EF

Mathematics

1 answer:

ElenaW [278]3 years ago

5 0

I would need to see a picture of the shape to get a idea on how to solve this

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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

djverab [1.8K]

I'll assume the ODE is

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

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

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

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

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

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

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

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

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

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

1 year ago

What percent is 24 of 96

inn [45]

You would get 4 percent.

4 0

2 years ago

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Does y=3^t represent growth or decay?

sweet [91]

Answer:

Decay

Step-by-step explanation:

5 0

2 years ago

I can’t remember how to do this if I try a bit longer I can probably figure it out but not sure exactly. Please If anyone can he

UNO [17]

Answer:

£2.38

Step-by-step explanation:

2.5 cost £1.40

4.25 cost £ x

so x=(4.25*1.40)/2.5=5.95/2.5=£2.38

5 0

2 years ago

Simplify the expression. 6(6) + 6(4)<br> a. 60<br> b. 10<br> c. 16<br> d. 12

Brums [2.3K]

60

Simplifying;
36+ 24
=60

4 0

3 years ago

Read 2 more answers