Consider the differential equation x²y" + xy + y = 0; cos(In(x)), sin(In(x)), (0, ∞o). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 5E
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Consider the differential equation
x²y" + xy' + y = 0; cos(In(x)), sin(In(x)), (0, ∞).
Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.
The functions satisfy the differential equation and are linearly independent since W(cos(In(x)), sin(In(x))) =
Form the general solution.
y =
#0 for 0 < x < 00.
Transcribed Image Text:Consider the differential equation x²y" + xy' + y = 0; cos(In(x)), sin(In(x)), (0, ∞). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(cos(In(x)), sin(In(x))) = Form the general solution. y = #0 for 0 < x < 00.
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