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Determine whether the given differential equation is exact.
1) Yes
2) No

User Ankor
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Final answer:

To determine whether the given differential equation is exact or not, we need to check if the coefficient of dx is the same as the partial derivative of the coefficient of x with respect to y, and if the coefficient of dy is the same as the partial derivative of the coefficient of y with respect to x. From the given equation, it can be observed that the coefficient of dx is µ\x and the coefficient of dy is v². To check if the equation is exact, we need to find the partial derivatives of µ\x with respect to y and v² with respect to x, and compare them with the respective coefficients. Therefore, based on the given information, the differential equation is not exact.

Step-by-step explanation:

A differential equation can be formed by letting the length of the mass element of the string approach zero, 1; (µ\x) v²} = 1/2 (µdx) v².

To determine whether the given differential equation is exact or not, we need to check if the coefficient of dx is the same as the partial derivative of the coefficient of x with respect to y, and if the coefficient of dy is the same as the partial derivative of the coefficient of y with respect to x.

From the given equation, it can be observed that the coefficient of dx is µ\x and the coefficient of dy is v². To check if the equation is exact, we need to find the partial derivatives of µ\x with respect to y and v² with respect to x, and compare them with the respective coefficients.

Therefore, based on the given information, the differential equation is not exact.

User Cmaughan
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