Question

Consider the initial value problem $$(8t^2 - 45t + 25) y'' - 3.5ty = \sin(0.5\pi t), y\left(\frac{45}{16}\right) = -3, y'\left(\frac{45}{16}\right) = 3.5.$$ On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply. $$(-\infty, \infty)$$ $$(0, 5)$$ $$\left(\frac{5}{8}, 5\right)$$ $$(-3, 3.5)$$ $$\left(\frac{55}{32}, \frac{125}{32}\right)$$

Name: consider the initial value problem 8t2 45t 25 y 35ty sin05pi t yleftfrac4516right 3 yleftfrac4516right 35 on which of these intervals is this initial value problem certain to have a unique t 93203
Uploaded: 2025-02-21T10:58:08-08:00
Duration: 4 min 36 s
Channel: Melissa Munoz
Description: consider the initial value problem 8t2 45t 25 y 35ty sin05pi t yleftfrac4516right 3 yleftfrac4516right 35 on which of these intervals is this initial value problem certain to have a unique t 93203

          Consider the initial value problem
$$(8t^2 - 45t + 25) y'' - 3.5ty = \sin(0.5\pi t), y\left(\frac{45}{16}\right) = -3, y'\left(\frac{45}{16}\right) = 3.5.$$
On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply.

$$(-\infty, \infty)$$
$$(0, 5)$$
$$\left(\frac{5}{8}, 5\right)$$
$$(-3, 3.5)$$
$$\left(\frac{55}{32}, \frac{125}{32}\right)$$

$consider the initial value problem 8t2 45t 25 y 35ty sin05pi t yleftfrac4516right 3 yleftfrac4516right 35 on which of these intervals is this initial value problem certain to have a unique t 93203$

Added by Brian M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Melissa Munoz

02/21/2025

Step 1

5ty = \sin(0.5\pi t)$$ We can rewrite this as $$y'' - \frac{3.5t}{8t^2 - 45t + 25} y = \frac{\sin(0.5\pi t)}{8t^2 - 45t + 25}$$ The coefficients are continuous everywhere except where $8t^2 - 45t + 25 = 0$. We can factor the quadratic as follows: $$8t^2 - 45t + 25 Show more…

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Consider the initial value problem $$(8t^2 - 45t + 25) y'' - 3.5ty = \sin(0.5\pi t), y\left(\frac{45}{16}\right) = -3, y'\left(\frac{45}{16}\right) = 3.5.$$ On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply. $$(-\infty, \infty)$$ $$(0, 5)$$ $$\left(\frac{5}{8}, 5\right)$$ $$(-3, 3.5)$$ $$\left(\frac{55}{32}, \frac{125}{32}\right)$$