Divide each term in by and simplify.

Multiply both sides by .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite the equation.

Set up an integral on each side.

The integral of with respect to is .

Integrate the right side.

Since is constant with respect to , move out of the integral.

The integral of with respect to is .

Simplify.

Group the constant of integration on the right side as .

Move all the terms containing a logarithm to the left side of the equation.

Simplify the left side.

Simplify .

Simplify each term.

Simplify by moving inside the logarithm.

Remove the absolute value in because exponentiations with even powers are always positive.

Use the quotient property of logarithms, .

To solve for , rewrite the equation using properties of logarithms.

Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .

Solve for .

Rewrite the equation as .

Multiply both sides by .

Simplify.

Simplify the left side.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify the right side.

Reorder factors in .

Remove the absolute value term. This creates a on the right side of the equation because .

Simplify the constant of integration.

Combine constants with the plus or minus.

Solve the Differential Equation x(dy)/(dx)=2y