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2 years ago

Cuantos terminos tiene -3xy

Mathematics

1 answer:

katrin [286]2 years ago

3 0

Answer:

El a+b tiene 1 terminó porque para separar un término el factor es el +Step-by-step explanation:

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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

Which equation is a point slope form equation for line AB ?

kap26 [50]

Answer:

$y-5=\frac{3}{4}(x-6)$

Step-by-step explanation:

we know that

The equation of a line in point slope form is equal to

$y-y1=m(x-x1)$

step 1

Find the slope m

we have the points

A(-2,-1),B(6,5)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{5+1}{6+2}$

$m=\frac{6}{8}$

simplify

$m=\frac{3}{4}$

step 2

Find the equation of the line

we have

$(x1,y1)=(6,5)$

$m=\frac{3}{4}$

substitute

$y-y1=m(x-x1)$

$y-5=\frac{3}{4}(x-6)$

3 0

3 years ago

DOES ANYONE KNOW THIS?????

dedylja [7]

Answer:

if i;m right its 45 degrees

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Calculate and express your answer in decimal form.

lapo4ka [179]

Hope this helps you :))))))

5 0

3 years ago

What is the slope of a line perpendicular to the line whose equation is 5x+6y=425x+6y=42. Fully reduce your answer.

Vlada [557]

Answer: m= 1/420

Step-by-step explanation:

5x + 6y - 6y - 425x = 42

5x -425x = 42

0 = -420x - 42

m = -420

slope of a perpendicular line = 1/420

if that helps.

3 0

3 years ago

Cuantos terminos tiene -3xy​

Cuantos terminos tiene -3xy