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1. (e²x + 4) dy = y dx

1. (e²x + 4) dy = y dx

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Obtain the general solution of the following differential equations.

1. (e²x + 4) dy = y dx 2. y dx + (1 - 3y)x dy = 3y dy 3. 2xyyy² - 2x³ 4. y(2xy² − 3) dx + (3x²y². 3x + 4y) dy = 0 5. y² dx + (3xy + y² − 1) dy = 0 6. y ln x ln y dx + dy = 0 7. u² dv = (4u² + 7uv + 2v² ) du 8. xy dx + (x² − 3y) dy = 0 - 9. (sin 02r cos² 0) dr + r cos 0(2r sin 0 + 1) d0 = 0 10. v² dx + x(x + v) dv 11. dx = 0 (1 + 2x tan y) dy = 0 12. t(s² + t²) ds — s(s² – t²) dt = 0
Transcribed Image Text:1. (e²x + 4) dy = y dx 2. y dx + (1 - 3y)x dy = 3y dy 3. 2xyyy² - 2x³ 4. y(2xy² − 3) dx + (3x²y². 3x + 4y) dy = 0 5. y² dx + (3xy + y² − 1) dy = 0 6. y ln x ln y dx + dy = 0 7. u² dv = (4u² + 7uv + 2v² ) du 8. xy dx + (x² − 3y) dy = 0 - 9. (sin 02r cos² 0) dr + r cos 0(2r sin 0 + 1) d0 = 0 10. v² dx + x(x + v) dv 11. dx = 0 (1 + 2x tan y) dy = 0 12. t(s² + t²) ds — s(s² – t²) dt = 0
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