The differential equation can be written in differential form: where M(x, y) -y-2y^7 y + 2y¹ = (y² + 6x) y' M(x, y) dx + N(x, y) dy = 0 , and N(x,? y) = y^4 + 6x The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by y7. Integrating that new equation, the solution of the differential equation is = C.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The differential equation
can be written in differential form:
where
M(x, y):
y + 2y¹ = (y² + 6x) y'
= -y-2y^7
M(x,y) dx + N(x, y) dy = 0
and N(x, y)
The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by y7. Integrating that new
equation, the solution of the differential equation is
= C.
y^4 + 6x
Transcribed Image Text:The differential equation can be written in differential form: where M(x, y): y + 2y¹ = (y² + 6x) y' = -y-2y^7 M(x,y) dx + N(x, y) dy = 0 and N(x, y) The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by y7. Integrating that new equation, the solution of the differential equation is = C. y^4 + 6x
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