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9. (a) Use the method of Lagrange multipliers to determine the minimum and maximu values of f(x, y) = x² + 3y² - 16y +5 on the circle x² + y² = 25. (b) Evaluate JS 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y = 3/x², y = x and y = 2x. dy (c) Solve the differential equation x² e-v/x - y² + xy- = =0 with y(1) = 0. dx

9. (a) Use the method of Lagrange multipliers to determine the minimum and maximu values of f(x, y) = x² + 3y² - 16y +5 on the circle x² + y² = 25. (b) Evaluate JS 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y = 3/x², y = x and y = 2x. dy (c) Solve the differential equation x² e-v/x - y² + xy- = =0 with y(1) = 0. dx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9. (a) Use the method of Lagrange multipliers to determine the minimum and maximum values of f(x, y) = x² + 3y² - 16y +5 on the circle x² + y² = 25. (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y = 3/x², y = x and y = 2x. D dy (c) Solve the differential equation x² e-v/x - y² + xy = 0 with y(1) = 0. dx
Transcribed Image Text:9. (a) Use the method of Lagrange multipliers to determine the minimum and maximum values of f(x, y) = x² + 3y² - 16y +5 on the circle x² + y² = 25. (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y = 3/x², y = x and y = 2x. D dy (c) Solve the differential equation x² e-v/x - y² + xy = 0 with y(1) = 0. dx
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