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

Question

f ′(s) = 14s − 12s^3, f(3) = 7

Answer 1

f ′(s) = 14s − 12s^3, f(3) = 7

Just integrate w.r.t s

f(s)=∫(14s-12s^3)ds+C, (c-constant)

f(s)=7s^2-3s^4+C,

Now we use the condition f(3)=7

7=7*3^2-3*3^4+C

C=3^5-8*7=..

Compute C and plug in into the equation

f(s)=7s^2-3s^4+,,



Answer 2