How do you solve the differential equation given f'(s)=6s−8s^3, f(2)=3?

erwachsenc6

erwachsenc6

Answered question

2022-10-12

How do you solve the differential equation given f ( s ) = 6 s - 8 s 3 ?

Answer & Explanation

dkmc4175fl

dkmc4175fl

Beginner2022-10-13Added 15 answers

Let y = f ( s ) d y d s = 6 s - 8 s 3
This is a first order separable DE, so we can separate the variables as follows:
d y = 6 s - 8 s 3 d s
Integrating gives:
y = 3 s 2 - 2 s 4 + C
We know f ( 2 ) = 3 3 = ( 3 ) ( 4 ) - ( 2 ) ( 16 ) + C
3 = 12 - 32 + C C = 23
Hence, the solution is:
y = 3 s 2 - 2 s 4 + 23

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