Problem #8: Consider the following initial value problem. $$ \frac{dy}{dx} = (y^2 - 10y + 16) \sin^2\left(\frac{2\pi y}{15}\right), \quad y(0) = a. $$ Give a possible value of the real number $a$ for which the solution to the corresponding initial value problem is a non-constant function that satisfies $$ \lim_{x\to\infty} y(x) = \frac{15}{2} $$ Problem #8: Just Save Submit Problem #8 for Grading Problem #8 Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Your Answer: Your Mark:
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We are looking for a value of $a$ such that the solution $y(x)$ is non-constant and satisfies $$ \lim_{x\to\infty} y(x) = \frac{15}{2} $$ Step 2: First, let's find the equilibrium points of the differential equation. Equilibrium points occur when $\frac{dy}{dx} = Show more…
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