(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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 11AEXP
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