For the differential equation y′′+4y′+4y=x3 part 1: solve the homogeneous equation the differential operator for the homogeneous equation is list the complementary functions (the functions that make up the complementary solution) . when you get this answer correct it will give you the format for the complementary solution that you must use below. part 2: find the particular solution to solve the non-homogeneous differential equation, we look for functions annihilated by the differential operator (a multiple of the operator given above) therefore the particular solution must be made up of the functions substituting these into the differential equation, we find the particular solution is part 3: solve the non-homogeneous equation y′′+4y′+4y=x3 has general solution (remember to use the format i gave you in your correct answer to the complementary functions above) now that we have the general solution solve the ivp y(0)=−6 y′(0)=8

1) The homogeneous equation is

with characteristic equation

which means we have the characteristic solution

The functions that make up this solution are and .

2) Several ways to do this. Using the method of undetermined coefficients, we suppose the particular takes the form

so that its derivatives are

Then substituting these into the ODE gives

Matching up the coefficients gives us the system

so the particular solution would be

3) The general solution is simply

Given the initial values and , we get

giving a particular solution to the IVP of

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.

can someone answer this question plz

step-by-step explanation: