Find the particular solution of the differential equation that satisfies the initial condition(s).

Question

f '(s) = 10s − 4s³,    f(3) = 5

Answer 1

f'(s) = 10s -4s^3

indefinite integral is:

F(s) = 5s^2 - s^4 + c where c = an unknown constant

using the other information f(3)=5 doesn't make sense

f(3) = 10(3) -4(3^)3 = 30--108= -78

-78 doesn't = 5

but if

F(3) =5

then 5^(3) -(3)^4 + c = 5

c = 5 +81-15 = 71

c=71

F(s) = 5s^2 -s^4 + 71

odds are the problem read F(3)=5, not f(3)=5