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

Find where .
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 .
Find where .
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 .
Check that .
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 .
Integrate to find .
Apply the constant rule.
Since the integral of will contain an integration constant, we can replace with .
Set .
Find .
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.
Solve for .
Move all terms not containing to the right side of the equation.
Find the antiderivative of to find .
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