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In order to solve with we first write and Setting We can solve for where to get and X-T/2 we find that Indeed, sin 2xdx + cos 3ydy = 0 y(π/2) = π/3 cos 3ydy= == sin 2xdz 1 sin 3y = cos 22+ It follows that 1 1 sin 3y=cos 2z+ = 2 = cos² (z). y=A- -aresin( arcsin (3 cos²z) 2z+c.

In order to solve with we first write and Setting We can solve for where to get and X-T/2 we find that Indeed, sin 2xdx + cos 3ydy = 0 y(π/2) = π/3 cos 3ydy= == sin 2xdz 1 sin 3y = cos 22+ It follows that 1 1 sin 3y=cos 2z+ = 2 = cos² (z). y=A- -aresin( arcsin (3 cos²z) 2z+c.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 29E
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and It follows from that the equation is Then we integrate After differentiating the last expression we obtain that Hence, we get where c is equal to again. y integrate c=1/2 differentiate y=π/3 exact 1 N = cos 3y. My = N₂ with respect to x to get 1 cos cos 2x + C(y). 1 sin 3y. C(y) sin 3y 1 2 sin(2x) cos 22 cos2x = c A=T/3 A=π/2 cos(2x) 3/4 1/2
Transcribed Image Text:and It follows from that the equation is Then we integrate After differentiating the last expression we obtain that Hence, we get where c is equal to again. y integrate c=1/2 differentiate y=π/3 exact 1 N = cos 3y. My = N₂ with respect to x to get 1 cos cos 2x + C(y). 1 sin 3y. C(y) sin 3y 1 2 sin(2x) cos 22 cos2x = c A=T/3 A=π/2 cos(2x) 3/4 1/2
In order to solve sin 2rdz + cos 3ydy = 0 with y(π/2) = π/3 we first write cos 3ydy = -sin 2rdz and 1 sin 3y = 1/cos 2z+c. Setting and x=T/2 we find that .It follows that 1 1 sin 3y = cos 2z+= cos² (2). We can solve for Indeed, y=A- arcsin (3 cos² z) where We can also solve this equation by using another method. We let to get 13 M = sin 2x
Transcribed Image Text:In order to solve sin 2rdz + cos 3ydy = 0 with y(π/2) = π/3 we first write cos 3ydy = -sin 2rdz and 1 sin 3y = 1/cos 2z+c. Setting and x=T/2 we find that .It follows that 1 1 sin 3y = cos 2z+= cos² (2). We can solve for Indeed, y=A- arcsin (3 cos² z) where We can also solve this equation by using another method. We let to get 13 M = sin 2x
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