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

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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Question

help number 5

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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