Find $$ f(x) $$ if $$ y=f(x) $$ satisfies $$ \frac{d y}{d x}=18 y x^{8} $$ and the $$ y $$-intercept of the curve $$ y=f(x) $$ is 3 $$ f(x)= $$

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1. Separate the variables:
   $$
   \frac{1}{y}\,dy = 18x^8\,dx.
   $$

2. Integrate both sides:
   $$
   \int \frac{1}{y}\,dy = \int 18x^8\,dx.
   $$
   The integrals yield:
   $$
   \ln|y| = 18 \cdot \frac{x^9}{9} + C,
   $$
   which simplifies to:
   $$
   \ln|y| = 2x^9 + C.
   $$

3. Exponentiate to solve for $$ y $$:
   $$
   |y| = e^{2x^9+C} = e^C \cdot e^{2x^9}.
   $$
   Let $$ A = e^C $$. Then:
   $$
   y = A e^{2x^9}.
   $$

4. Use the initial condition $$ f(0)=3 $$ to find $$ A $$:
   $$
   3 = A e^{2\cdot0^9} = A e^0 = A \quad \Longrightarrow \quad A = 3.
   $$

5. Write the final function:
   $$
   f(x)=3e^{2x^9}.
   $$
$$ f(x) = 3e^{2x^9} $$

Find if satisfies

and the -intercept of the curve is 3

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Find if satisfies and the -intercept of the curve is 3