Problem: Solve the following differential equation: <mtable columnalign="right center left" ro

Sylvia Byrd 2022-07-07 Answered
Problem:
Solve the following differential equation:
6 x 2 y d x ( x 3 + 1 ) d y = 0
Answer:
This is a separable differential equation.
6 x 2 x 3 + 1 d x d y y = 0 6 x 2 x 3 + 1 d x d y y = c 1 2 ln | x 3 + 1 | ln | y | = c 1 ln ( x 3 + 1 ) 2 ln | y | = c 1 ln ( ( x 3 + 1 ) 2 | y | ) = c 1 ( x 3 + 1 ) 2 = c | y |
However, the book gets:
( x 3 + 1 ) 2 = | c y |
Is my answer different from the book's answer? I believe it is.
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Answers (1)

fugprurgeil
Answered 2022-07-08 Author has 12 answers
Both answers are correct.
Your answer
( x 3 + 1 ) 2 = c | y |
makes the assumption that c 0
The book's answer
( x 3 + 1 ) 2 = | c y |
is OK for all values of c.
Thus to make sure that you can take any value for c go with the book's answer, otherwise mention that c 0

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