Final answer to the problem
$\ln\left(\csc\left(x-y\right)+\cot\left(x-y\right)\right)=-y+C_0$
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Step-by-step Solution
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation dx/dy=sin(x-y). When we identify that a differential equation has an expression of the form Ax+By+C, we can apply a linear substitution in order to simplify it to a separable equation. We can identify that x-y has the form Ax+By+C. Let's define a new variable u and set it equal to the expression. Isolate the dependent variable x. Differentiate both sides of the equation with respect to the independent variable y. Now, substitute x-y and \frac{dx}{dy} on the original differential equation. We will see that it results in a separable equation that we can easily solve.
Final answer to the problem
$\ln\left(\csc\left(x-y\right)+\cot\left(x-y\right)\right)=-y+C_0$
