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

step-by-step explanation:

first you will have to convert 3/4 into a decimal

which is .75

then you will have to divide 1.5 by .75

which is 2

no you have to divide

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0