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We are given the following nonhomogeneous differential equation. y"8y' + 20y 200x2 - 78xex To find the general solution, we first find the complementary function y for the associated homogenous equation y" - 8y' + 20y = 0. Then we find a particular solution y, for the nonhomogeneous equation, which is determined by the form of g(x) = 200x278xex. The general solution is then found as the sum y = y + Yp First, we must find the roots of the auxiliary equation for y" - 8y' + 20y = 0. m2 8m + 20 = 0 Solving for m, the roots of the auxiliary equation are as follows. positive imaginary part m₁ = negative imaginary part m₂ =

We are given the following nonhomogeneous differential equation. y"8y' + 20y 200x2 - 78xex To find the general solution, we first find the complementary function y for the associated homogenous equation y" - 8y' + 20y = 0. Then we find a particular solution y, for the nonhomogeneous equation, which is determined by the form of g(x) = 200x278xex. The general solution is then found as the sum y = y + Yp First, we must find the roots of the auxiliary equation for y" - 8y' + 20y = 0. m2 8m + 20 = 0 Solving for m, the roots of the auxiliary equation are as follows. positive imaginary part m₁ = negative imaginary part m₂ =

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter4: Linear Functions
Section: Chapter Questions
Problem 1PT: Determine whether the following algebraic equationcan be written as a linear function. 2x+3y=7
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GN5-STEP1 Please answer the question thank yo!

Find linearly independent functions that are annihilated by the given differential operator. (Give as many functions as possible. Use x as the independent variable. Enter your answers as a comma-separated list.) D3 18D2 + 81D
Transcribed Image Text:Find linearly independent functions that are annihilated by the given differential operator. (Give as many functions as possible. Use x as the independent variable. Enter your answers as a comma-separated list.) D3 18D2 + 81D
Step 1 We are given the following nonhomogeneous differential equation. y" - 8y' + 20y = 200x² - 78xex To find the general solution, we first find the complementary function y for the associated homogenous equation y" – 8y' + 20y = 0. Then we find a particular solution equation, which is determined by the form of g(x) = 200x² – 78xex. The general solution is then found as the sum y = y₁ + Yp First, we must find the roots of the auxiliary equation for y" - 8y' + 20y = 0. m² 8m + 20 = 0 Solving for m, the roots of the auxiliary equation are as follows. positive imaginary part negative imaginary part m₁ = m₂ = Ур for the nonhomogeneous
Transcribed Image Text:Step 1 We are given the following nonhomogeneous differential equation. y" - 8y' + 20y = 200x² - 78xex To find the general solution, we first find the complementary function y for the associated homogenous equation y" – 8y' + 20y = 0. Then we find a particular solution equation, which is determined by the form of g(x) = 200x² – 78xex. The general solution is then found as the sum y = y₁ + Yp First, we must find the roots of the auxiliary equation for y" - 8y' + 20y = 0. m² 8m + 20 = 0 Solving for m, the roots of the auxiliary equation are as follows. positive imaginary part negative imaginary part m₁ = m₂ = Ур for the nonhomogeneous
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