Differentiate with respect to .

By the Sum Rule, the derivative of with respect to is .

Since is constant with respect to , the derivative of with respect to is .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Subtract from .

Differentiate with respect to .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Substitute for and for .

Since the two sides have been shown to be equivalent, the equation is an identity.

is an identity.

is an identity.

Set equal to the integral of .

Apply the constant rule.

Since the integral of will contain an integration constant, we can replace with .

Set .

Differentiate with respect to .

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Differentiate using the function rule which states that the derivative of is .

Reorder terms.

Move all terms not containing to the right side of the equation.

Integrate both sides of .

Evaluate .

By the Power Rule, the integral of with respect to is .

Substitute for in .

Simplify .

Solve the Differential Equation (x-y)dx-xdy=0