What is the solution for f^'(s)=10s-12s^3,f(3)=2 ?

The solution for f^'(s)=10s-12s^3,f(3)=2 is f(s)=5s^2-3s^4+200

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f^'(s)=10s-12s^3,f(3)=2

f^{^{'}} (s) = 10 s - 12 s^{3}, f (3) = 2

f (s) = 5 s^{2} - 3 s^{4} + 200

Solution steps

f^{'} (s) = 10 s - 12 s^{3}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (s) = \int 10 s - 12 s^{3} d s

\int 10 s - 12 s^{3} d s = 5 s^{2} - 3 s^{4} + c_{1}

f (s) = 5 s^{2} - 3 s^{4} + c_{1}

Apply initial conditions:

f (s) = 5 s^{2} - 3 s^{4} + 200

f (s) = 5 s^{2} - 3 s^{4} + 200

n = 0 \sum \infty x^{2 n}

y = x^{2} + 1, (2, 5)

\frac{d}{d t} (e^{7 t})

\int \frac{1}{( x + 5 ) 10 x + x ^{2}} d x

\int 9 - x^{2} d x

What is the solution for f^'(s)=10s-12s^3,f(3)=2 ?
The solution for f^'(s)=10s-12s^3,f(3)=2 is f(s)=5s^2-3s^4+200