Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
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Textbook Question
Chapter 17.1, Problem 1PT
True or False:
(x + y)y″ + (x − 10)y′ + xy + 10 = 0 is homogeneous.
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Chapter 17 Solutions
Study Guide for Stewart's Multivariable Calculus, 8th
Ch. 17.1 - True or False: (x + y)y + (x 10)y + xy + 10 = 0...Ch. 17.1 - Prob. 2PTCh. 17.1 - Prob. 3PTCh. 17.1 - The solution to y 10y + 25y = 0, y(0) = 5, y(1) =...Ch. 17.1 - True or False: An initial-value problem specifies...Ch. 17.1 - Prob. 6PTCh. 17.2 - Prob. 1PTCh. 17.2 - Prob. 2PTCh. 17.2 - Prob. 3PTCh. 17.2 - Prob. 4PT
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
9. find the solution of the problem with given initial value, using homogeneous equations with constant coefficients.
y''+y'-2y=0, y(0)=1, y'(0)=1
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Find the general solution of the 2nd order non-homogeneous DE using methods of undetermined coefficient:
y” - 2y’- 8y = 2xex
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Given the differential equation (4x2+y2)dx + x(x-2y)dy = 0
1. Verify that M(x,y) = (4x2 + y2) and N(x,y) = x(x-2y) are homogeneous functions.
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Find the general solution using reduction of order.
1. x2y''-xy'+y=0, y1=ln(x)
2. y''=ln(x)
3. y''+y'=cos(4x)
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Linear Homogeneous DE with Constant Coefficients
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Find the general solution to the DE, given that y1(t) = t+1 and y2(t) =et are solutions of the corresponding homogeneous equation.
y"-(1+1/t)y'+1/y=t
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Find the homogeneous solution to the second order constant coefficient ODE’s. Solution must be real.
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Find the general solution of the 2nd order non-homogeneous DE using variation of parameters:
y” - 2y’- 8y = 2xex
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Given that φ(x,y)=x-1y-3 is an integrating factor for the given DE, what is the general solution of the DE?
x3y3 dx + x (1 + y2) dy = 0
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Consider the differential equation: (56x^2)y″−16x(x+7)y′+16(x+7)y=5x3, x>0.
You can verify that y1=2x and y2=5xexp(2x/7) satisfy the corresponding homogeneous equation.
Compute the Wronskian W between y1 and y2
Apply variation of parameters to find a particular solution.
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1. When is separation of variables applicable?
2. How can homogeneous equations be distinguished?
3. When is the exact method applicable?
4. Why is there a need to solve for integrating factors?
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3. find the given general differential solution, using homogeneous equations with constant coefficients.
6y''-y'-y=0
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