dy 3 Use the method of separation of variables to find the solution to =y dx dy= dx Begin by separating the variables.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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In applications, most initial value problems will have a unique solution. In fact, the existence of unique solutions is so important that there is
dy
Əf
a theorem about the existence and uniqueness of a solution. Consider the initial value problem = f(x,y), y(x) = yo. Iff and are
dx
ду
continuous functions in some rectangle R = {(x,y):a<x<b, c<y<d} that contains the point (xo.Yo), then the initial value problem has a
unique solution (x) in some interval x₁ -8<x<xo +8, where ô is a positive number. The method for separable equations can give a
1
dy 3
solution, but it may not give all the solutions. To illustrate this, consider the equation=y. Answer parts (a) through (d).
(a) Use the method of separation of variables to find the solution to
dy =
dx
58
=
1
3
Begin by separating the variables.
Transcribed Image Text:In applications, most initial value problems will have a unique solution. In fact, the existence of unique solutions is so important that there is dy Əf a theorem about the existence and uniqueness of a solution. Consider the initial value problem = f(x,y), y(x) = yo. Iff and are dx ду continuous functions in some rectangle R = {(x,y):a<x<b, c<y<d} that contains the point (xo.Yo), then the initial value problem has a unique solution (x) in some interval x₁ -8<x<xo +8, where ô is a positive number. The method for separable equations can give a 1 dy 3 solution, but it may not give all the solutions. To illustrate this, consider the equation=y. Answer parts (a) through (d). (a) Use the method of separation of variables to find the solution to dy = dx 58 = 1 3 Begin by separating the variables.
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