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Chapter 8: Q41P (page 430)
Solve by use of Fourier series. Assume in each case that the right-hand side is a periodic function whose values are stated for one period.
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Answer
The solution of is .
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Using Problems 29 and 31b, show that equation (6.24) is correct.
Several Terms on the Right-Hand Side: Principle of Superposition So far we have brushed over a question which may have occurred to you: What do we do if there are several terms on the right-hand side of the equation involving different exponentials?
In Problem 33 to 38 , solve the given differential equations by using the principle of superposition [see the solution of equation (6.29) . For example, in Problem 33 , solve three differential equations with right-hand sides equal to the three different brackets. Note that terms with the same exponential factor are kept together; thus a polynomial of any degree is kept together in one bracket.
If P dollars are left in the bank at interest I percent per year compounded continuously, find the amount A at time t. Hint: Find dA, the interest on A dollars for time dt.
In Problem 33 to 38, solve the given differential equations by using the principle of superposition [see the solution of equation (6.29)]. For example, in Problem 33, solve three differential equations with right-hand sides equal to the three different brackets. Note that terms with the same exponential factor are kept together; thus, a polynomial of any degree is kept together in one bracket.
In Problem 33 to 38, solve the given differential equations by using the principle of superposition [see the solution of equation (6.29)]. For example, in Problem 33, solve three differential equations with right-hand sides equal to the three different brackets. Note that terms with the same exponential factor are kept together; thus, a polynomial of any degree is kept together in one bracket.
Find the orthogonal trajectories of each of the following families of curves. In each case, sketch or computer plot several of the given curves and several of their orthogonal trajectories. Be careful to eliminate the constant from for the original curves; this constant takes different values for different curves of the original family, and you want an expression for which is valid for all curves of the family crossed by the orthogonal trajectory you are trying to find. See equations to
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