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 =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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GN5-STEP1 Please answer the question thank yo!
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
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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