linear in x and has a solution equal to xel G(V)dy = ƒ H (y) eJ G(Y)dydy + C dx Using linear first order differential equation, solve for the general solution of dy x(2-у) Please y show complete solutions.
linear in x and has a solution equal to xel G(V)dy = ƒ H (y) eJ G(Y)dydy + C dx Using linear first order differential equation, solve for the general solution of dy x(2-у) Please y show complete solutions.
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:A linear first order differential equation is of the first degree in the dependent variable and its derivative.
The general form of a first order differential equation linear in
dy
y
is
dx
+ P(x)y = Q(x) where P and Q
are functions of x only.
dy
Consider
dx
+ P(x)y = Q(x), then its solution is ye! PG
P(x)dx = [ Q(x) es P(x)dx dx + C.
dx
Also,
+ G(y)x = H(y), where G and H are functions of y only, is a first order differential equation
dy
linear in x and has a solution equal to xel G(y)dy = SH(y) e G(y)dydy + C
dx
Using linear first order differential equation, solve for the general solution of
dy
x(2-у)
1
Please
y
show complete solutions.
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