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WRite the analytical solution for this equation: dy/dx=f(x,y)=x2-3y.;y(0)=2 check the attached photo for the format

WRite the analytical solution for this equation: dy/dx=f(x,y)=x2-3y.;y(0)=2 check the attached photo for the format

Calculus: Early Transcendentals
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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WRite the analytical solution for this equation:

dy/dx=f(x,y)=x2-3y.;y(0)=2

check the attached photo for the format.

 

 

dy = f(x,y) = 3x – 2y with y(0) = 0 %3D dx Analytical Solution: dy + 2y = 3x dx v = e2x e*y = 3 xe2*dx + C хе2xdx + C Let u = x; du = dx v = [*a 1 =-e 2 3 e2x dx + C 2 3 -e2x + C ==(2xe2x – e2x) + C 4 V = e2xdx e2xy =5xe24 -- 3 3 et*y =xe* -* + C =(2xe* – e*) + C 4 3 y =-(2x – 1) + Ce-2x; y(0) = 0 4 3 0 ==(2·0 – 1) + Ceº; C = . 4 3 4 3 y =(2x – 1) +e-2* +-e-2x 4 4
Transcribed Image Text:dy = f(x,y) = 3x – 2y with y(0) = 0 %3D dx Analytical Solution: dy + 2y = 3x dx v = e2x e*y = 3 xe2*dx + C хе2xdx + C Let u = x; du = dx v = [*a 1 =-e 2 3 e2x dx + C 2 3 -e2x + C ==(2xe2x – e2x) + C 4 V = e2xdx e2xy =5xe24 -- 3 3 et*y =xe* -* + C =(2xe* – e*) + C 4 3 y =-(2x – 1) + Ce-2x; y(0) = 0 4 3 0 ==(2·0 – 1) + Ceº; C = . 4 3 4 3 y =(2x – 1) +e-2* +-e-2x 4 4
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