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1-3x dy for y = In dx a) Find the derivative x+2 b) Given yosx = 3x. dy By taking natural logarithm on both sides, find in terms of x and y. dx c) If y= f(x) is given implicitly as 2x – xy + y = 5, show that dy (2y–x)+2| dy - 2 +4 = 0. dx dx² dx d) Parametric equations of a curve are given as 1 and y=t+- 4 x = 2t d²y where t + 0. Evaluate the value of when t = -4. dx?

1-3x dy for y = In dx a) Find the derivative x+2 b) Given yosx = 3x. dy By taking natural logarithm on both sides, find in terms of x and y. dx c) If y= f(x) is given implicitly as 2x – xy + y = 5, show that dy (2y–x)+2| dy - 2 +4 = 0. dx dx² dx d) Parametric equations of a curve are given as 1 and y=t+- 4 x = 2t d²y where t + 0. Evaluate the value of when t = -4. 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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dy for y = In dx 1-3x a) Find the derivative x+2 b) Given ycosx = 3x°. By taking natural logarithm on both sides, find in terms of x and y . dx c) If y = f(x) is given implicitly as 2x – xy + y = 5, show that dy dx dy (2y–x)dy -2 +4 = 0. +2 dx? dx d) Parametric equations of a curve are given as 1 and y =t+-, 4 x = 2t d'y where t + 0. Evaluate the value of when t = -4. dx?
Transcribed Image Text:dy for y = In dx 1-3x a) Find the derivative x+2 b) Given ycosx = 3x°. By taking natural logarithm on both sides, find in terms of x and y . dx c) If y = f(x) is given implicitly as 2x – xy + y = 5, show that dy dx dy (2y–x)dy -2 +4 = 0. +2 dx? dx d) Parametric equations of a curve are given as 1 and y =t+-, 4 x = 2t d'y where t + 0. Evaluate the value of when t = -4. dx?
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