Consider the differential equation x°y" + 12x3y" + 25xy' – 25y = 0; x, x, x In(x), (0, 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(x, x5, x In(x)) = * 0 for 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the differential equation
x°y" + 12x3y" + 25xy' – 25y = 0; x, x, x In(x), (0, 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(x, x5, x In(x)) =
* 0 for 0 <x< 0o0.
Form the general solution.
y =
Transcribed Image Text:Consider the differential equation x°y" + 12x3y" + 25xy' – 25y = 0; x, x, x In(x), (0, 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(x, x5, x In(x)) = * 0 for 0 <x< 0o0. Form the general solution. y =
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