Factor out of .

Factor out of .

Factor out of .

Factor out of .

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.

Integrate the left side.

Let . Then . Rewrite using and .

Let . Find .

Differentiate .

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

Differentiate using the Power Rule which states that is where .

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

Add and .

Rewrite the problem using and .

The integral of with respect to is .

Replace all occurrences of with .

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

Group the constant of integration on the right side as .

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 .

Combine and .

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

Add to both sides of the equation.

Rewrite as .

Reorder and .

Combine constants with the plus or minus.

Solve the Differential Equation (dy)/(dx)=xy-4x