N- My If = R, where R is a function depending only on the quantity z = xy, then the differential equation хМ — уN M + Ny = 0 has an integrating factor of the form R(z)dz µ(z) Find an integrating factor and solve the given equation. (3x² 9y\ dy 9х + y = 0 dx + 5x2 H(xy) = ху 3xy+ + 3y3 = C 2 5x µ(xy) = xy, 3x²y + + 3y = c 2 5x µ(xy) xy' 3x y + + 3y3 = C 2 5x2 И(ху) %3D ху, Зх3 у+ + 3y = c 2 5x2 H(xy) = 3x°y + 1 3xy + ху + 3y = 2
N- My If = R, where R is a function depending only on the quantity z = xy, then the differential equation хМ — уN M + Ny = 0 has an integrating factor of the form R(z)dz µ(z) Find an integrating factor and solve the given equation. (3x² 9y\ dy 9х + y = 0 dx + 5x2 H(xy) = ху 3xy+ + 3y3 = C 2 5x µ(xy) = xy, 3x²y + + 3y = c 2 5x µ(xy) xy' 3x y + + 3y3 = C 2 5x2 И(ху) %3D ху, Зх3 у+ + 3y = c 2 5x2 H(xy) = 3x°y + 1 3xy + ху + 3y = 2
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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Transcribed Image Text:N- My
If
= R, where R is a function depending only on the quantity z = xy, then the differential equation
хМ — уN
M + Ny = 0
has an integrating factor of the form
R(z)dz
µ(z)
Find an integrating factor and solve the given equation.
(3x²
9y\ dy
9х +
y
= 0
dx
+
5x2
H(xy) =
ху
3xy+
+ 3y3
= C
2
5x
µ(xy) = xy, 3x²y +
+ 3y = c
2
5x
µ(xy)
xy'
3x y +
+ 3y3
= C
2
5x2
И(ху) %3D ху, Зх3 у+
+ 3y = c
2
H(xy) = 3x°y +
1
3x²y +
xy
5x2
+ 3y = c
2
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