7t 101 y" – 7y' +10 = 0: y= c1e" + c2 + Steps y" - 7y + 10 = 0 Second order linear non - homogeneous differential equation with constant coefficients Hide Definition A second order linear, non - homogeneous ODE has the form of ay" + by' + cy = g(x) Show Steps Rewrite in the form of a Second order linear non - homogeneous ODE y" – 7y' = -10 The general solution to a(x)y" + b(x)y' +c(x)y=g(x) can be written as y=Vh+Yp Yh is the solution to the homogeneous ODE a(x)y" + b(x)y' + c(x)y=0 Yp, the particular solution, is any function that satisfies the non - homogeneous equation 7t Show Steps Find y, by solving y" – 7y' = 0: y= c1e“ + c2
7t 101 y" – 7y' +10 = 0: y= c1e" + c2 + Steps y" - 7y + 10 = 0 Second order linear non - homogeneous differential equation with constant coefficients Hide Definition A second order linear, non - homogeneous ODE has the form of ay" + by' + cy = g(x) Show Steps Rewrite in the form of a Second order linear non - homogeneous ODE y" – 7y' = -10 The general solution to a(x)y" + b(x)y' +c(x)y=g(x) can be written as y=Vh+Yp Yh is the solution to the homogeneous ODE a(x)y" + b(x)y' + c(x)y=0 Yp, the particular solution, is any function that satisfies the non - homogeneous equation 7t Show Steps Find y, by solving y" – 7y' = 0: y= c1e“ + c2
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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Show, expand and explain the solution in the first image. Show the complete solution. And get as well the constants using the conditions in second image.
Transcribed Image Text:7t
101
y" – 7y' +10 = 0: y= c1e" + c2 +
Steps
y" - 7y + 10 = 0
Second order linear non - homogeneous differential equation with constant coefficients Hide Definition
A second order linear, non - homogeneous ODE has the form of ay" + by' + cy = g(x)
Show Steps
Rewrite in the form of a Second order linear non - homogeneous ODE
y" – 7y' = -10
The general solution to a(x)y" + b(x)y' +c(x)y=g(x) can be written as
y=Vh+Yp
Yh is the solution to the homogeneous ODE a(x)y" + b(x)y' + c(x)y = 0
Yp, the particular solution, is any function that satisfies the non - homogeneous equation
Show Steps
Find y, by solving y" – 7y' = 0: y= cje" + c2
Show Steps
101
Find y, that satisfies y" – Ty' = -10: y =
The general solution y = yh +Yp is:
y = cqe" + c2 + 0
101
y = cje" + c2 +
Transcribed Image Text:y" – 7y' + 10 = 0, y(0) = 2 and y' (0) = 4
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