revitprojectb7

revitprojectb7

Answered

2022-09-28

Find the general solution of ( d y d x ) = y 2 - 4 ?

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Answer & Explanation

Helena Bentley

Helena Bentley

Expert

2022-09-29Added 10 answers

This is separable:
d y y 2 - 4 = d x
And
1 y 2 - 4 = 1 4 ( 1 y - 2 - 1 y + 2 )
Which leaves you with:
1 4   1 y - 2 - 1 y + 2   d y =   d x
ln | y - 2 | - ln | y + 2 | = 4 x + C
| y - 2 | | y + 2 | = C e 4 x
For y>2 or y<−2, that's:
y - 2 y + 2 = C e 4 x
Otherwise it's:
y - 2 y + 2 = - C e 4 x , ie just some constant with a different sign.
So proceeding with C:
y - 2 y + 2 = C e 4 x y = 2   1 + C e 4 x 1 - C e 4 x

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