**MATH - DIFFERENTIAL EQUATION**

Solve the questions below:

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2).

Image transcriptions

Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) X (1 + In(x) + _) dx = (2 - In(x)) dy Need Help? Read It Watch It

Consider the following differential equation. (sin(y) - y sin(x)) dx + (cos(x) + x cos(y) - y) dy = 0 Let M = sin(y) - y sin(x) and / = cos(x) + x cos(y) - y. Find the following partial derivatives. N. of Let = sin(y) - y sin(x). Integrate each term of this partial derivative with respect to x, letting h(y) be an unknown function in y. ax R( x, y) = + h( y) Find the derivative of h(y). h'(y) = Is the given differential equation exact? O Yes O No Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.)

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