Find the particular solution that satisfies the differential equation and the initial condition.

Question

Find the particular solution that satisfies the differential equation and the initial condition.

 

 

1. f '(x) = 8x,    f(0) = 7

 

 

 

2.  f '(s) = 14s − 12s3,    f(3) = 1

Answer 1

1)

 

Anti-derive f'(x) to find f(x).

 

f(x) = 4x² + C

 

where C is the constant to solve for using the 2nd condition.

 

7 = 4(0)² + C

 

7 = C

 

f(x) = 4x² + 7

 

 

Can you try the next one on your own?