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2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the reduction of order method to find the second linearly independent solution. Finally, write the general solution of the DE. a. 2t²y" + ty - 3y = 0, b. 4x²y" + y = 0, y₁ (t) = t-¹. x² ln x, y₁ (x): = x2 x > 0.

2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the reduction of order method to find the second linearly independent solution. Finally, write the general solution of the DE. a. 2t²y" + ty - 3y = 0, b. 4x²y" + y = 0, y₁ (t) = t-¹. x² ln x, y₁ (x): = x2 x > 0.

Calculus For The Life Sciences
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.CR: Chapter 11 Review
Problem 5CR
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2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the reduction of order method to find the second linearly independent solution. Finally, write the general solution of the DE. a. 2t²y" +ty' − 3y = 0, b. 4x²y" + y = 0, y₁ (t) = t-¹. 3₁(x) = x² ln x. x > 0.
Transcribed Image Text:2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the reduction of order method to find the second linearly independent solution. Finally, write the general solution of the DE. a. 2t²y" +ty' − 3y = 0, b. 4x²y" + y = 0, y₁ (t) = t-¹. 3₁(x) = x² ln x. x > 0.
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