All categories

3 years ago

Determine whether the given function is a solution to the given differential equation. y=cosx+x8, d^2y/dx^2 + y = x^8 + 56x^6.

Mathematics

1 answer:

Ulleksa [173]3 years ago

4 0

The correct question is:

Determine whether the given function is a solution to the given differential equation. y = cosx + x^8; d²y/dx² + y = x^8 + 56x^6

Step-by-step explanation:

Given the differential equation

d²y/dx² + y = x^8 + 56x^6.

Suppose y = cosx + x^8 is a solution, then differentiating y twice, and adding it to itself, must give the value on the right hand side of the differential equation.

Let us differentiate y twice

y = cosx + x^8

dy/dx = -sinx + 8x^7

d²y/dx² = -cosx + 56x^6

Now,

d²y/dx² + y = -cosx + 56x^6 + cosx + x^8

= 56x^6 + x^8

Therefore,

d²y/dx² + y = x^8 + 56x^6

Which shows that y = cosx + x^8 is a solution to the differential equation.

You might be interested in

If a || b, m<2=63°, and m<9=105°, find the measure of missing angle m<1=?

worty [1.4K]

Given:

a.) ∠9 = 105°

b.) ∠2 = 63°

Step 1: Determine the measure of ∠10.

∠9 and ∠10 are Supplementary Angles. This means that the sum of the two angles is equal to 180°.

From this, we generate the following equation:

$\text{ }\angle9\text{ + }\angle10=180^{\circ}$

Let's then now proceed to find out the measure of ∠10.

$\text{ }\angle9\text{ + }\angle10=180^{\circ}$ $\text{ }105^{\circ}\text{ + }\angle10=180^{\circ}$ $\angle10=180^{\circ}\text{ - }105^{\circ}$ $\angle10=75^{\circ}$

Step 2: Determine the measure of ∠3.

∠10 and ∠3 are Alternate Exterior Angles. Under this, the two angles must be congruent.

$\text{ }\angle3\text{ = }\angle10$

Therefore,

$\text{ }\angle3\text{ = }\angle10$ $\text{ }\angle3=75^{\circ}$

Step 3: Determine the measure of ∠1.

∠1, ∠2 and ∠3 are also Supplementary Angles. This means that the sum of the three angles is equal to 180°.

Thus, we generate the equation below:

$\text{ }\angle1\text{ + }\angle2\text{ + }\angle3=180^{\circ}$

Let's now find the measure of ∠1,

$\text{ }\angle1\text{ + }\angle2\text{ + }\angle3=180^{\circ}$ $\text{ }\angle1\text{ + }63^{\circ}\text{ + }75^{\circ}=180^{\circ}$ $\text{ }\angle1\text{ + }138^{\circ}=180^{\circ}$ $\text{ }\angle1\text{ }=180^{\circ}\text{ - }138^{\circ}$ $\text{ }\angle1\text{ }=42^{\circ}$

Therefore, the measure of ∠1 is 42°.

8 0

1 year ago

HELLLP TAKING A FINAL

Musya8 [376]

Answer:

2: For every gallon of gas purchased, $3.75 was paid.

Step-by-step explanation:

Both options 1 and 3 would require having a dot plotted at those points to be sure, and they're close but they're still approximations. And option 4 is irrelevant. However the point at (4,15) can be used to check option two: 15/4 = 3.75 , ie the price per gallon of gas.

6 0

2 years ago

Read 2 more answers

A machine can produce a maximum of 600 parts per day. Yesterday, it produced 75 % of its maximum capacity. How many parts did th

gizmo_the_mogwai [7]

Answer:

450

Step-by-step explanation:

here is a fast way:

1- 75% = 75/100 = 3/4

2- 600 × (3/4) = 450

8 0