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5. Find the General and Particular solution of Зу ; у%3D 3, when x 3D 0 %3D 业

5. Find the General and Particular solution of Зу ; у%3D 3, when x 3D 0 %3D 业

Advanced Engineering Mathematics
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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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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