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Sagot :
Particular solution of the differential equation that satisfies the initial condition f'(s) = 10s - 4s³ , f(3) = 5 is f(s) = 5s² - s⁴ + 41.
We determine the particular solution to the differential equation. We do this by integrating the given differential equation and then applying the given initial condition. The power rule should be used for the given expression.
[tex]\int\ {x^{a} } \, dx[/tex] = [tex]\frac{x^{a+1} }{a+1} }[/tex]
we have given that,
f'(s) = 10s - 4s³
f(s) = ∫ f'(s)ds
= ∫(10s - 4s³)ds
= [tex]\frac{10s^{2} }{2} - \frac{4s^{2} }{4}+ C[/tex]
f(s) = 5s² - s⁴ + C
Now we will apply the initial condition,
f(3) = 5
⇒5(3)² - (3)⁴ + C =5
-36 + C = 5
C =41
Therefore the solution is expressed as,
f(s) = 5s² - s⁴ + 41
This is the particular solution.
Given question is incomplete. Complete question is given as:
find the particular solution of the differential equation that satisfies the initial condition(s). f '(s) = 10s - 4s³, f(3) = 5.
To know more about particular solution here
https://brainly.com/question/10622045
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