Write these differential equations in the form y" + p(t)y = g(t), then classify them as homogeneous ornonhomogeneous.t(a) = +13y5(b) y' (4y + 8t)(tant) = 6-(c) yy' - 7ty² = 0

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Answered: Write these differential equations in…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Put the differential equation p(t) = g(t) = ty' (t² + 5)y cos(t) + e3t into the form y' + p(t)y = g(t) and find p(t) and g(t). Y help (formulas) help (formulas)
Match the differential equation with its direction field. y' = 8(x + y) – 1 y Q.2 10 0.1 0.1 -0.3 -0.2-0.1 0.1 0.2 -0,3- I -Q.31 +0,2 -0.1 0.1 0,2 0,3 0.1 //// //// //////// o for o < x < T/8, 0 < y < T/8. O y' = 8(x + y) - 1 = 0 on the line y = -x + 1/8, and y' = -1 on the line y = -x. O y' = 8(x + y) - 1 = 0 on the lines x = 0 and y = 8. O The slopes at each point are independent of y, so the slopes are the same along each line parallel to the y-axis. Note that for y = 8, y' = 0. O The slopes at each point are independent of x, so the slopes are the same along each line parallel to the x-axis. Note that for y = 8, y' = 0.
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Given the differential equation = 2x (y² + 1) dy dx 5. (a) Sketch the slope field for this differential equation at the points shown in the figure. (-1,1) (0,1) (1,1) (-1,0) (0,0) (1,0) (-1,-1) (0,-1) (1,-1) (b) Let f be the particular solution to the differential equation whose graph passes through (0,1). Express f as a function of x, and state its domain.

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Write these differential equations in the form y" + p(t)y = g(t), then classify them as homogeneous or nonhomogeneous. t 5 (a) 3y (b) y' - (4y + 8t) (tant) = 6 (c) yy' - 7ty² = 0 = +1