Solve the system for the exact special solution y = y(x): (keep the fraction and the square root without decimals.) 1. ydx + x[ in(x) - in(y) - 1]dy = 0 and y(1) = e for in(e) = 1.

Assume a solution of the form . Differentiating both sides gives

with and .

Divide both sides by and we have

Notice that

so the ODE is exact. Now we can look for a solution with

Integrating the first PDE with respect to gives

and differentiating this with respect to gives

So this ODE has general solution

Given that , we have

so the particular solution is

i think it's ф or x=6,-6

step-by-step explanation:

-x^2=-36

x^2=-36

ф

or

if you mean by : -(x^2)=-36

it'll be: x^2=36

x=6,x=-6

hope it'll ! have a good day!

you for asking!

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: