The differential equation can be written in differential form: y − 4y³ = (y² + 2x)y' M(x, y) dx+N(x, y) dy = 0 where M(x, y) = N(x, y) = -☐ help (formulas), and = help (formulas) The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by y³. Integrating that new equation, the solution of the differential equation is = constant. help (formulas) Book: Section 1.8 of Notes on Diffy Qs

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:
y − 4y³ = (y² + 2x)y'
M(x, y) dx+N(x, y) dy = 0
where
M(x, y) =
N(x, y)
=
-☐
help (formulas), and
=
help (formulas)
The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by y³.
Integrating that new equation, the solution of the differential equation is
=
constant. help (formulas)
Book: Section 1.8 of Notes on Diffy Qs
Transcribed Image Text:The differential equation can be written in differential form: y − 4y³ = (y² + 2x)y' M(x, y) dx+N(x, y) dy = 0 where M(x, y) = N(x, y) = -☐ help (formulas), and = help (formulas) The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by y³. Integrating that new equation, the solution of the differential equation is = constant. help (formulas) Book: Section 1.8 of Notes on Diffy Qs
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