Calculus: Early Transcendental Functions - 6 Edition - Chapter 16.1 - Problem 13
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# ?Solving an Exact Differential Equation In Exercises 5-14, determine whether the differential equation is exact. If it is,find the general solution.

Calculus: Early Transcendental Functions | 6th Edition

Problem 13

Solving an Exact Differential Equation In Exercises 5-14, determine whether the differential equation is exact. If it is,find the general solution.

$$\frac{1}{(x-y)^{2}}\left(y^{2} d x+x^{2} d y\right)=0$$

Text Transcription:

1/(x-y)^2 (y^2 dx+x^2 dy)=0

Accepted Solution
Step-by-Step Solution:

Step 1 of 5) The integral is L 1 0 L 1 x L y-x 0 F(x, y, z) dz dy dx. For example, if F(x, y, z) = 1, we would find the volume of the tetrahedron to be V = L 1 0 L 1 x L y-x 0 dz dy dx = L 1 0 L 1 x ( y - x) dy dx = L 1 0 c12 y2 - xy d y=x y=1 dx = L 1 0 a12 - x + 1 2 x2b dx = c12 x - 1 2 x2 + 1 6 x3 d 0 1 = 1 6 . We get the same result by integrating with the order dy dz dx. From Example 2,

###### Chapter 16.1, Problem 13 is Solved

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