Solve the differential equation x^3y"' - 3x^2 y" 6xy'-6y = 0.

Equation at the end of step 1 : (((x3) •y) - (((3x2•y6) •x) •y)) - 6y = 0 Step 2 : Step 3 : Pulling out like terms:

3.1 Pull out like factors:

-3x3y7 + x3y - 6y = - y • (3x3y6 - x3 + 6)

Trying to factor a multi variable polynomial:

3.2 Factoring 3x3y6 - x3 + 6

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Equation at the end of step 3 : - y • (3x3y6 - x3 + 6) = 0 Step 4 : Theory - Roots of a product:

4.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

4.2 Solve : - y = 0

Multiply both sides of the equation by (-1) : y = 0