The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution y2(x) of the homogeneous equation and a particular solution yp(x) of the given nonhomogeneous equation. y'' − 3y' + 2y = 7e3x; y1 = ex

Step-by-step explanation

Standard form

Hence your P(t) = -3, Q(t) = 2

After replacing all y", y' and y to homogeneous part, you will have

because

Let U = V'

.

Replace back,

then

So, general solution of the ODE is

Particular solution is just take derivative of the general one twice and plug back into the original ODE to find A and B

You can finish it by yourself. Let me know if you need more help

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

eve and marks ratios are equivalent

step-by-step explanation: