dy To solve a first order linear equation + P(x)y=Q(x), one can multiply both sides by dx dy 1 an integrating factor e and solve it. By saying so, solve +y=3x.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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To solve a first order linear equation
dy
+ P(x)y Q(x), one can multiply both sides by
dx
an integrating factor e and solve it. By saying so, solve
dy 1
-+-y=3x.
(a) A homogenous equation of the first order and degree is one which can be written in
the form
dx
= f(2). Show that
dy
x2+y?
%3D
is a homogenous equation.
%3D
dx
2x2
dy
x²+y?
(b) Solve
dx
by using the substitution y = vx.
%3D
2x2
Transcribed Image Text:To solve a first order linear equation dy + P(x)y Q(x), one can multiply both sides by dx an integrating factor e and solve it. By saying so, solve dy 1 -+-y=3x. (a) A homogenous equation of the first order and degree is one which can be written in the form dx = f(2). Show that dy x2+y? %3D is a homogenous equation. %3D dx 2x2 dy x²+y? (b) Solve dx by using the substitution y = vx. %3D 2x2
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