Hello, I attached a picture of my question. I am having a lot of trouble getting the answer.
Consider the following initial-value problem.
. . .\(\displaystyle \dfrac{dy}{dx}\, =\, \left(y^2\, -\, 9y\, +\, 8\right)\,\sin^2\left(\dfrac{2\pi y}{15}\right),\qquad y(0)\, =\, a\)
Give a possible value for the real number a for which the solution to the corresponding initial-value problem is a non-constant function that satisfied the following:
. . .\(\displaystyle \displaystyle \lim_{x \rightarrow \infty}\, y(x)\, =\, \dfrac{15}{2}\)
I thought that a would simply be 15/2 because of Picard's theorem but this is incorrect and I do not understand why.
Consider the following initial-value problem.
. . .\(\displaystyle \dfrac{dy}{dx}\, =\, \left(y^2\, -\, 9y\, +\, 8\right)\,\sin^2\left(\dfrac{2\pi y}{15}\right),\qquad y(0)\, =\, a\)
Give a possible value for the real number a for which the solution to the corresponding initial-value problem is a non-constant function that satisfied the following:
. . .\(\displaystyle \displaystyle \lim_{x \rightarrow \infty}\, y(x)\, =\, \dfrac{15}{2}\)
I thought that a would simply be 15/2 because of Picard's theorem but this is incorrect and I do not understand why.
Last edited by a moderator: