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Concept explainers
Reduction of order Suppose you are solving a second-order linear homogeneous
a. Verify that y1 = t is a solution. Assume the second homogeneous solution is y2 and it has the form
b. Substitute y2 into the differential equation and simplify the resulting equation to show that v satisfies the equation
c. Note that this equation is first order in v′; so let w = v′ to obtain the first-order equation
d. Solve this separable equation and show that
e. Now solve the equation
f. Finally, recall that y2(t) = v(t)t and conclude that the second solution is y2(t) = c1 t ln t.
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Chapter D2 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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