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(a) Determine whether each of the following equations is exact. If it is exact, find the solution. (a1). (3x² - 2xy +2) + (6y² − x² + 3) y' = 0 My = -2x and Ny = -2x so the equation is exact. 4 = √ 3x² - 2xy +2dx = x³ + x²y + 2x + h(y) and thus 4y = x²+h' (y) = 6y² = x² +3. - Therefore h' (y) = 6y² + 3 and h(y) = 2y³ + 3y + C. The final solution is x3 + x²y+2x+2y³ + 3y = c where c is arbitrary constant.

(a) Determine whether each of the following equations is exact. If it is exact, find the solution. (a1). (3x² - 2xy +2) + (6y² − x² + 3) y' = 0 My = -2x and Ny = -2x so the equation is exact. 4 = √ 3x² - 2xy +2dx = x³ + x²y + 2x + h(y) and thus 4y = x²+h' (y) = 6y² = x² +3. - Therefore h' (y) = 6y² + 3 and h(y) = 2y³ + 3y + C. The final solution is x3 + x²y+2x+2y³ + 3y = c where c is arbitrary constant.

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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(a) Determine whether each of the following equations is exact. If it is exact, find the solution. (a1). (3x² - 2xy +2) + (6y² − x² + 3) y' = 0 My = -2x and Ny = -2x so the equation is exact. 4 = √ 3x² - 2xy +2dx = x³ + x²y + 2x + h(y) and thus 4y = x²+h' (y) = 6y² = x² +3. - Therefore h' (y) = 6y² + 3 and h(y) = 2y³ + 3y + C. The final solution is x3 + x²y+2x+2y³ + 3y = c where c is arbitrary constant.
Transcribed Image Text:(a) Determine whether each of the following equations is exact. If it is exact, find the solution. (a1). (3x² - 2xy +2) + (6y² − x² + 3) y' = 0 My = -2x and Ny = -2x so the equation is exact. 4 = √ 3x² - 2xy +2dx = x³ + x²y + 2x + h(y) and thus 4y = x²+h' (y) = 6y² = x² +3. - Therefore h' (y) = 6y² + 3 and h(y) = 2y³ + 3y + C. The final solution is x3 + x²y+2x+2y³ + 3y = c where c is arbitrary constant.
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