3. given the differential equation y"+y= 0 and the set of two functions sint-cost, sint + cost, show that this a fundamental set of functions for the equation, and note the interval(s) over which this is true. wken (osxsihx | cos sint

Answer with explanation:

Given the differential equation

y''+y=0

The two function let

Differentiate

Then we get

Because

We find wronskin to prove that the function  is independent/ fundamental function.

w(x)=

Hence, the given two function are fundamental set of function on R.

1: -2 3/4, -2 1/2, -14, 0, 3, 8 1/3

2: -4, -3, -2 1/2, -2 1/4, 3 1/4,

step-by-step explanation:

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.