Answer:
So, solution of the differential equation is

Step-by-step explanation:
We have the given differential equation: y′′+4y=5xcos(2x)
We use the Method of Undetermined Coefficients.
We first solve the homogeneous differential equation y′′+4y=0.

It is a homogeneous solution:

Now, we finding a particular solution.

we get

So, solution of the differential equation is

Answer:
x² - 2x - 2
By Completing the Square....
x² - 2x + 1² - 2 - 1²
(x - 1)² - 3 .....
Hope it helps.
The given expression is

We have to find the discriminant first . And for that, first we need to move whole terms of the left side to right side, that is


The formula of discriminant is

Substituting the values of a,b and c, we will get

And since the discriminant is greater than 0, or it is positive so we have two real roots.
Therefore the correct option is B .
Answer:
No, it is not a right triangle.
Step-by-step explanation:
Given:
The sides of the triangle = 15 10 and 7
To Find:
Whether the triangle is a right triangle = ?
Solution:
According to Pythagorean theorem , In an right triangle the the sum of the squares of the two smaller sides must equal to the square of the larger side

where
a and b are the smaller sides
c is the larger side
Now from the given data, lets assume
a = 10 and b =7 and c =15
Substituting in the above equation we get,

100 + 49 = 225
149 = 225

So, the given triangle is not a right triangle.