Use the method of reduction of order to find a second solution of the given differential equation. Find the general solution y(x) of the differential equation. Verify that y(x) is indeed the general solution by showing that y(x) is a linear combination of two solutions y₁ and y2 whose Wronskian is nonzero. x²y" + xy' + (x² - 0.25)y = 0 x > 0 Y₁(x) = x-¹/² sin x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Use the method of reduction of order to find a second solution of the given differential equation. Find the general
solution y(x) of the differential equation. Verify that y(x) is indeed the general solution by showing that y(x) is
a linear combination of two solutions y₁ and y2 whose Wronskian is nonzero.
x²y" + xy' + (x² - 0.25)y = 0
x > 0
y₁(x) = x-1/² sin x
Transcribed Image Text:Use the method of reduction of order to find a second solution of the given differential equation. Find the general solution y(x) of the differential equation. Verify that y(x) is indeed the general solution by showing that y(x) is a linear combination of two solutions y₁ and y2 whose Wronskian is nonzero. x²y" + xy' + (x² - 0.25)y = 0 x > 0 y₁(x) = x-1/² sin x
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