Solve the differential equation by variation of parameters, subject to the initial conditions y(0) = 1, y'(0) = 0. 36y'' − y = xex/6

The homogeneous ODE

has characteristic equation

with roots at , and admits two linearly independent solutions,

as the Wronskian is

Variation of parameters has us looking for solutions of the form

such that

We have

and we get

The general solution is

The initial conditions tell us

so that the particular solution is

i would need to see the dot plot : )

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.