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pshichka [43]
3 years ago
10

Anyone know the answer?​

Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
5 0
I’m pretty sure it’s d but i’m not 100%
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Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).
I am Lyosha [343]
Take the homogeneous part and find the roots to the characteristic equation:

y''+4y=0\implies r^2+4=0\implies r=\pm2i

This means the characteristic solution is y_c=C_1\cos2x+C_2\sin2x.

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form y_p=ax\cos2x+bx\sin2x. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With y_1=\cos2x and y_2=\sin2x, you're looking for a particular solution of the form y_p=u_1y_1+u_2y_2. The functions u_i satisfy

u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx
u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx

where W(y_1,y_2) is the Wronskian determinant of the two characteristic solutions.

W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2

So you have

u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx
u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x

u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx
u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x

So you end up with a solution

u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x

but since \cos2x is already accounted for in the characteristic solution, the particular solution is then

y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x

so that the general solution is

y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x
7 0
3 years ago
Find the slope of the line that passes through two points (-6,2) (-4, -8).
Ksenya-84 [330]

Answer:

the answer is m=-5

Step-by-step explanation:

Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.

hope this helps :)

5 0
2 years ago
3. A kite is aloft at the end of a 1500 foot string. The string make an angle of 43° with the
sineoko [7]

Answer:

h= 1500\,*\,sin(43^o)

Step-by-step explanation:

Notice that there is a right angle triangle formed with sides as follows:

hypotenuse is the actual 1500 ft string. The acute angle 43 degrees is opposite to the segment that represents the height of the kite from the ground. Therefore, the trigonometric ratio that we can use to find that opposite side to the given angle, is the sine function as shown below:

sin(43^o) = \frac{opposite}{hypotenuse} \\sin(43^o) = \frac{opposite}{1500}\\opposite = 1500\,*\,sin(43^o)\\h= 1500\,*\,sin(43^o)

8 0
3 years ago
The sum of 2 consecutive integers is -33.If n is the first integer,which equation best models the situation?
monitta

Answer:

You can choose which equation below suits your taste but I recommend the 2n + 1 = -33.

Step-by-step explanation:

(n) + (n + 1) =  - 33 \\ 2n + 1 =  - 33 \\ 2n =  - 32 \\ n =  - 16

5 0
3 years ago
Each cube in this figure is a -centimeter unit cube. How many cubes are in the prism? [Type your answer as a number.]
Annette [7]

Answer:

72 cubes

Step-by-step explanation:

One face of the cube has 12 cubes. A cube has 6 faces, 12 × 6 = 72. (12 cubes × 6 faces = 72 cubes)

6 0
2 years ago
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