8) use reduction of order to solve. one solution of homogeneo x2y" +7xy' +5y =x 1 x> 0 y1 = x here y1 is a solution of the corresponding homogeneous.

I suspect there's a typo in the question, because is *not* a solution to the corresponding homogeneous equation. We have and , so the ODE reduces to

Let , then and , and substituting these into the (homogeneous) ODE gives

which then admits the characteristic solutions and .

Now to find a solution to the non-homogeneous ODE. We look for a solution of the form or .

It doesn't matter which one we start with, so let's use the first case. We get derivatives and . Substituting into the ODE yields

Substitute , so that and

which is linear in , and we can condense the left side as the derivative of a product after multiplying both sides by :

Integrate to solve for :

Then multiply both sides by to solve for :

so we found another fundamental solution that satisifes this ODE.

ruth is 6 years old

step-by-step explanation:

6 + 24 = 30,   so 6/30 = .2  

if you do 1/5 it also equals .2, so that is the answer.

42%

step-by-step explanation:

we know,

total people = 60

total males = 25

percentage of males

= 25/60 × 100

= 25/6 × 10

= 25/3 × 5

= 125 / 3

= 41.

rounding of = 42%

happy to

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