First change to standard form of first order linear differential equation and then by finding the appropriate integrating factor find a particular solution for the initial value problem:xy' + y = lnx ; y(e)=1

Step-by-step explanation:

Given is a Differential equation as

To bring it to linear form we can divide the full equation by x

This is of the form

y'+p(x) *y = q(x)

p(x) = 1/x

So find

Solution is

Use the initial value as y(e) =1

So solution is

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: