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Suppose is another solution. Then
Substituting these derivatives into the ODE gives
Let , so that
Then the ODE becomes
and we can condense the left hand side as a derivative of a product,
Integrate both sides with respect to :
Solve for :
Solve for :
So another linearly independent solution is .
Answer:
Given Polynomial:
Factors of Coefficient of terms
80 = 5 × 16
32 = 2 × 16
48 = 3 × 16
Common factor of the coefficient of all term is 16.
Each term contain variable. So the Minimum power of b is common from all terms.
Common from all variable part comes b².
So, Common factor of the polynomial = 16b²
⇒ 16b² ( 5b² ) - 16b² ( 2c³ ) + 16b² ( 3b²c )
⇒ 16b² ( 5b² - 2c³ + 3b²c )
Therefore, Statements that are true about David's word are:
The GCF of the coefficients is correct.
The variable c is not common to all terms, so a power of c should not have been factored out.
In step 6, David applied the distributive property