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  • Pregunta: In Problems 1–20 determine whether the given differential equation is exact. If it is exact, solve it. 1. (2x – 1) dx + (3y + 7) dy = 0 2. (2x + y) dx - (x + 6y) dy = 0 3. (5x + 4y) dx + (4x – 8y3) dy = 0 4. (sin y - y sin x) dx + (cos x + x cos y - y) dy = 0 5. (2xy2 – 3) dx + (2x²y + 4) dy = 0 6. (2y = + cos 3x) x + 2 - 4x + 3y sin 3x = 0 7. (x2 - y2) dx +

    student submitted image, transcription available below

    student submitted image, transcription available below

    Only 7 and 22

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    Note: As per chegg guidlines, I am only solving Question 7.

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Texto de la transcripción de la imagen:
In Problems 1–20 determine whether the given differential equation is exact. If it is exact, solve it. 1. (2x – 1) dx + (3y + 7) dy = 0 2. (2x + y) dx - (x + 6y) dy = 0 3. (5x + 4y) dx + (4x – 8y3) dy = 0 4. (sin y - y sin x) dx + (cos x + x cos y - y) dy = 0 5. (2xy2 – 3) dx + (2x²y + 4) dy = 0 6. (2y = + cos 3x) x + 2 - 4x + 3y sin 3x = 0 7. (x2 - y2) dx + (x2 – 2xy) dy = 0 8. (1 + ln x++) dx = (1 – In ») dy 11 + ln x + - (1 – In x) dy In Problems 21–26 solve the given initial-value problem. 21. (x + y)2 dx + (2xy + x2 – 1) dy = 0, y(1) = 1 22. (ex + y) dx + (2 + x + ye") dy = 0, y(0) = 1 23. (4y + 2t – 5) dt + (6y + 4t – 1) dy = 0, y(-1) = 2 24. (**") + 2 = 0, x1) = 1 25. (y2 cos x – 3x²y – 2x) dx + (2y sin x - x3 + In y) dy = 0, y(0) = e