10 Short answers and 20 multiple choice. Hope this helps. :)
Yesterday and another of her homework?
Standard reduction of order procedure: suppose there is a second solution of the form

, which has derivatives



Substitute these terms into the ODE:



and replacing

, we have an ODE linear in

:

Divide both sides by

, giving

and noting that the left hand side is a derivative of a product, namely
![\dfrac{\mathrm d}{\mathrm dx}[wx]=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bwx%5D%3D0)
we can then integrate both sides to obtain


Solve for

:


Now

where the second term is already accounted for by

, which means

, and the above is the general solution for the ODE.
Answer:
9/25
Step-by-step explanation:
Number of student who has cat , dog = 25 - 3 = 22
Number of students who has cat and dogs = (15 + 16) - 22
= 31 - 22 = 9
Number of students who has only cats = 15 - 9 = 6
Number of students who has only dogs = 16 - 9 = 7
P(Cat & dog) = 9/25