Q2 Consider nonnegative integer solutions of the equation x_1+x_2+x_3+x_4+x_5+x_6=30x1+x2+x3+x4+x5+x6=30. Q2.1 How many different solutions are there? Q2.2 How many solutions also satisfy: for every i\in \{ 1,2,3,4,5,6\}i∈{1,2,3,4,5,6}, x_ixi is positive and even?

Q2 Consider nonnegative integer solutions of the equation x_1+x_2+x_3+x_4+x_5+x_6=30x1+x2+x3+x4+x5+x6=30. Q2.1 How many different solutions are there? Q2.2 How many solutions also satisfy: for every i\in \{ 1,2,3,4,5,6\}i∈{1,2,3,4,5,6}, x_ixi is positive and even?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider nonnegative integer solutions of the equation x_1+x_2+x_3+x_4+x_5+x_6=30x1+x2+x3+x4+x5+x6=30.

Q2.1

How many different solutions are there?

Q2.2

How many solutions also satisfy: for every i\in \{ 1,2,3,4,5,6\}i∈{1,2,3,4,5,6}, x_ixi is positive and even?

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