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3 years ago

Select one: A. Supplementary B. Vertical C. Complementary D. Acute

Mathematics

1 answer:

Rom4ik [11]3 years ago

5 0

Shouldnt there be a picture or something?

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Find a particular solution to y" - y + y = 2 sin(3x)

leonid [27]

Answer with explanation:

The given differential equation is

y" -y'+y=2 sin 3x------(1)

Let, y'=z

y"=z'

$\frac{dy}{dx}=z\\\\d y=zdx\\\\y=z x$

Substituting the value of , y, y' and y" in equation (1)

z'-z+zx=2 sin 3 x

z'+z(x-1)=2 sin 3 x-----------(1)

This is a type of linear differential equation.

Integrating factor

$=e^{\int (x-1) dx}\\\\=e^{\frac{x^2}{2}-x}$

Multiplying both sides of equation (1) by integrating factor and integrating we get

$\rightarrow z\times e^{\frac{x^2}{2}-x}=\int 2 sin 3 x \times e^{\frac{x^2}{2}-x} dx=I$

$I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx -\int \frac{2\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx-\frac{2I}{3}\\\\\frac{5I}{3}=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{5}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{5} dx$

8 0

2 years ago

Never been good at similar figures.. xP

Otrada [13]

1 is false, 2 is true, 3 is false, 4 is false

5 0

2 years ago

What is ∑n=15[5(−2)n−1] equal to?

kicyunya [14]

Answer:

Although the notation is sloppy, I will assume based on former questions of the same that "∑n=15[5(−2)^n−1]" translates mathematically to . Please correct me, though, if this in incorrect.

Anyway, there is neat formula that will deal with question very quickly. It is the following:

Sn is the sum of the geometric series

a1 is the first term in the series

r is the common ratio

n is the number of terms in the finite geometric series

Let's use this formula to our advantage! However, there are two variables that we do not know: a1 and n. Let's start with a1.The first term in the series is when n=1, so let's determine what that is.

6 0

2 years ago

Determine the solution to the system of equations below. x-3y=1 3x-5y=11

EastWind [94]

The answer you are looking for is (7, 2).

5 0

3 years ago

Is -root 16 a rational number

aleksklad [387]

Answer:

yes ! it's a rational number.

Step-by-step explanation:

The square root of 16 is 4, which is an integer, and therefore rational.

Hope it'll help!

stay safe:)

7 0

3 years ago

Read 2 more answers