Ask question

Ask question

All categories

allochka39001 [22]

3 years ago

10

Find the general solution for differential equation (D4 - 5D3 + 5D2 + 5D - 6)y = 0

1 answer:

Anastaziya [24]3 years ago

6 0

Given differential equation, (D<span>4 </span>- 5D3<span> + 5D</span>2<span> + 5D - 6)y = 0</span>

=> For general solution of equation,

Solve D<span>4 </span>- 5D3<span> + 5D</span>2<span> + 5D - 6 = 0</span>

=> D<span>4 </span>- 5D3<span> + 6D</span>2<span> - D</span><span>2 </span>+ 5D - 6 = 0

=> D2<span> (D</span>2<span> - 5D + 6) - (D</span>2<span> - 5D + 6) = 0</span>

=> (D2<span> - 5D + 6)(D</span>2<span> - 1) = 0 ................................(1)</span>

<span>Now </span>

D<span>2 </span><span>- 1 = (D - 1)(D + 1) and </span>

Factors of D2<span> - 5D + 6</span>

D2<span> - 5D + 6 = D</span>2<span> - 2D - 3D + 6</span>

= D(D - 2) - 3(D - 2)

= (D - 3)(D - 2)

Therefore, equation (1) implies

(D2<span> - 5D + 6)(D</span>2<span> - 1) = (D - 3)(D - 2)(D - 1)(D + 1) = 0</span>

=> D = 3, 2, 1, -1 or D = -1, 1,, 2, 3

=> General solution of differential equation is,<span>

=><span> y = C1 e-x + C2 ex + C3 e2x + C4 e3x</span> .
</span>

You might be interested in

Ashley is preparing for a horse riding competition. She has trained her horse for 5 hours and has completed 195 rounds. At what

allochka39001 [22]

Answer:

1:39

Step-by-step explanation:

195 divided by 5 is 1:39.

4 0

3 years ago

Read 2 more answers

Please help me <br>i beg you <br>PLEASE HELP ME ASAP <br><br>I SWEAR TO GOD WILL MARK YOU BRAINIEST

daser333 [38]

Step-by-step explanation:

DEFINITION: Besting: the clockwise totation (0° to 360°) from North to any line.

A) Calculate the bearings of D from A:

bearings of D from A =x

looking the picture:

x=48°+55°+180°

x+103°+180°

x=283°

B)Calculate the bearings of A from C:

bearings of A from C =y

180°+55°=y

y=235°

C) Calculate the distance between A and B:

The angle in B is 74° (Because 55°+51°+74°=180°)

Using the Law of sines:

$\frac{19}{sin(74)} =\frac{AB}{sin(51)} \\\\AB=19sin(51)sin(74)\\AB=14,2\\\\$

D)Calculate the distance between D and C:

Using the Law of cossines:

$DC^{2} =27^{2} +19^{2} -2*27*19*cos(48)\\DC=20,09$

E) A Helicopter is hovering at A at a height of 2.5Km, find angle of elevation of helicopter from C:

The triangle HBA is rectangle

$\alpha =arctan(\frac{2,5}{19})$

α=7,49°

5 0

2 years ago

I need some help.. fraction: {5⁷}{5²}

Anvisha [2.4K]

Step-by-step explanation:

$\dfrac{5^7}{5^2}\qquad|\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=5^{7-2}=5^5$

3 0

3 years ago

Veronica brought her turtle out of its aquarium for 15 minutes every night for 7 days how many total minutes did she bring her t

mestny [16]

Answer: Total minutes she brought her turtle out of this aquarium = 105 minutes

Explanation :

Since we have given that

Time for which Veronica brought her turtle out of its aquarium = 15 minutes

Number of days she did so = 7

Total time in a week she did so is given by

$15\times 7 = 105\text{ minutes }$

So , Total minutes she brought her turtle out of this aquarium = 105 minutes.

4 0

3 years ago

PLEASE HELP. A cylinder shaped water tank has a diameter of 8 m and a height of 20 m. What volume of water does the tank contain

anyanavicka [17]

Your answer is 602.88

4 0

3 years ago

Read 2 more answers