Solve the initial value problem.y" - 5y"-9y' +45y = 0;The solution is y(t) =y(0) = 6, y'(0) = 14, y'(0) = 118 Find three linearly independent solutions of the given third-order differential equation and write a general solution asan arbitrary linear combination of them.z""+72" +82'-16z = 0A general solution is z(t) =

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Answered: Solve the initial value problem. y'' -…

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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Solve: y''' — 5y'' — y' + 5y = 0 y(0) y(t) = = – 6, y'(0) = − 16, y’’(0) = − 78
The average adult takes about 12 breaths per minute. As a patient inhales, the volume of air in the lung increases. As the patient exhales, the volume of air in the lung decreases. For t in seconds since start of the breathing cycle, the volume of air inhaled or exhaled since t = 0 is given,' in hundreds of cubic centimeters, by 2n A(t) = - 2cos 5 + 2. (a) How long is one breathing cycle? i seconds (b) Find A' (3) and explain what it means. Round your answer to three decimal places. A' (3) = i hundred cubic centimeters/second.
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As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the dx differential equation =1.6x-0.004x² (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If x=50 when t=0, how long will it take for an additional 50 g of salt to dissolve? (a) The maximum amount of the salt that will ever dissolve in the methanol is gijams. (Simplify your answer.) 5 AI 9 IN F5 F6 2 8 # B - U dt F7 → = ∞ A View an example Get more help. ↓ F8 H i 8 ↑ 2 e B F9 ↑ T' l Y F10 + + 1 8 *** F11 √i co Less F12 ● S Vi 2 Ө ÷ 1, A = Clear all L PRISC INS X U SCRLK - O HOME C V € Σ PAUSE PG UP 8 FR v -W. Check answer NUM (88) A S i x
y''' — 4y'' + 13y' + 50y y(0) = 4, y'(0) = 10, y’’(0) = 42 y(t) = = 0

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Solve the initial value problem. y'' - 5y" -9y' +45y = 0; The solution is y(t) = - y(0) = 6, y'(0)=14, y'(0)=118