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Section 2.1 Integrating Factor: Problem 5 (1 point) Solve the initial value problem $8\left(\sin(t)\frac{dy}{dt} + \cos(t)y\right) = \cos(t)\sin^2(t)$, for $0 < t < \pi$ and $y(\frac{\pi}{2}) = 14$. Put the problem in standard form, Then find the integrating factor, $p(t) = \boxed{\text{ }}$ and finally find $y(t) = \boxed{\text{ }}$

          Section 2.1 Integrating Factor: Problem 5
(1 point)
Solve the initial value problem
$8\left(\sin(t)\frac{dy}{dt} + \cos(t)y\right) = \cos(t)\sin^2(t)$, 
for $0 < t < \pi$ and $y(\frac{\pi}{2}) = 14$.
Put the problem in standard form,
Then find the integrating factor, $p(t) = \boxed{\text{ }}$
and finally find $y(t) = \boxed{\text{ }}$

Show more…

Section 2.1 Integrating Factor: Problem 5
(1 point)
Solve the initial value problem
8(sin(t)(dy)/(dt) + cos(t)y) = cos(t)sin^2(t),
for 0 < t < π and y((π)/(2)) = 14.
Put the problem in standard form,
Then find the integrating factor, p(t) =
and finally find y(t) =

Added by Sara B.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Eduard Sanchez

Step 1

First, we can rewrite the equation as $\frac{dy}{dt} = \frac{1}{4t} - \frac{y}{2t}$. Show more…

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Solve the initial value problem $\frac{dy}{dt} + \frac{y}{2t} = \frac{1}{4t}$, $y(0) = 1$

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