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Linear Algebra
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. ...
Verified Answer:
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) ...
Verified Answer:
In Example 2 we found that the coefficient matrix ...
Question: 11.1.4
Solve the equation y″ + y = 0. ...
Verified Answer:
If we assume a solution of the form
y = \su...
Question: 11.1.3
Solve the equation x²y′ = y – x – 1. ...
Verified Answer:
We make the usual substitutions
y = \sum{c_...
Question: 11.1.2
Solve the equation (x – 3)y′ + 2y = 0. ...
Verified Answer:
As before, we substitute
y = \sum\limits_{n...
Question: 11.1.1
Solve the equation y′ + 2y = 0. ...
Verified Answer:
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) ...
Verified Answer:
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) ...
Verified Answer:
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) ...
Verified Answer:
We make the usual substitution of the power series...
Question: 11.2.6
Solve the initial value problem (t² – 2t – 3)d²y/dt² + 3(t – 1)dy/dt + y = 0; y(1) = 4, y′(1) = -1. (14) ...
Verified Answer:
We need a general solution of the form
\sum...
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