###### Differential Equations and Linear Algebra

183 SOLVED PROBLEMS

Question: 3.6.11

## Apply the formula in (23) to find the inverse of the matrix A =[1 4 5 4 2 5 -3 3 -1] of Example 10, in which we saw that |A| = 29. ...

First we calculate the cofactors of A, arranging o...
Question: 7.6.3

## Find a general solution of the system x′ = [1 -3 3 7]x. (20) ...

In Example 2 we found that the coefficient matrix ...
Question: 11.1.4

## Solve the equation y″ + y = 0. ...

If we assume a solution of the form y = \su...
Question: 11.1.3

## Solve the equation x²y′ = y – x – 1. ...

We make the usual substitutions y = \sum{c_...
Question: 11.1.2

## Solve the equation (x – 3)y′ + 2y = 0. ...

As before, we substitute y = \sum\limits_{n...
Question: 11.1.1

## Solve the equation y′ + 2y = 0. ...

We substitute the series y = \sum\limits_{n...
Question: 11.3.5

## Find a Frobenius solution of Bessel’s equation of order zero, x²y″ + xy′ + x²y = 0. (28) ...

In the form of (17), Eq. (28) becomes y^{″}...
Question: 11.3.4

## Find the Frobenius series solutions of 2x²y″ + 3xy′ – (x² + 1)y = 0. (20) ...

First we divide each term by 2x² to put the equati...
Question: 11.2.7

## Find two linearly independent solutions of y″ – xy′ – x²y = 0. (15) ...

We need a general solution of the form \sum...