Is this an exact Differential equation or not [(x+y)sin(y)]dx+[xsin(y)+cos(y)]dy=0

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Q: 1.1.2 - Show all work please.

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Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.