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y' = x +6y

y' = x +6y

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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1. Complete the table below. Order Degree Ordinary or Partial Linear or Non- Independent Dependent Variable Linear Variable y' = x +6y y" = 4y +y3 3 d²y dy dx2 + 3 = 0 dx y" +2xy' +4y = %3D cos2x dy х2-1 dx y+4 ди dv + aw + ду a²u ax az 20²u at2 ax2 2. Verify that the function y = Ciex + C2e2× is a solution of the differential equation y" – 3y' + 2y = 0 3. Is y(x) = Cısin2x + C2cos2x, where C1 and C2 are arbitrary constants, a solution of y" + 4y = 0? 4. Find the General and Particular solution of dy = -8 sin 4x ; y= 6 when x = 0 dx dy 5. Find the General and Particular solution of = 3y ; y= 3, when x = %3| dx
Transcribed Image Text:1. Complete the table below. Order Degree Ordinary or Partial Linear or Non- Independent Dependent Variable Linear Variable y' = x +6y y" = 4y +y3 3 d²y dy dx2 + 3 = 0 dx y" +2xy' +4y = %3D cos2x dy х2-1 dx y+4 ди dv + aw + ду a²u ax az 20²u at2 ax2 2. Verify that the function y = Ciex + C2e2× is a solution of the differential equation y" – 3y' + 2y = 0 3. Is y(x) = Cısin2x + C2cos2x, where C1 and C2 are arbitrary constants, a solution of y" + 4y = 0? 4. Find the General and Particular solution of dy = -8 sin 4x ; y= 6 when x = 0 dx dy 5. Find the General and Particular solution of = 3y ; y= 3, when x = %3| dx
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