# Show that the one parameter family of straight lines u = Ct + f(C) is

Content type
User Generated
Rating
Showing Page:
1/1
Show that the one-parameter family of straight lines u =
Ct + f(C) is a solution to the differential equation t du/dt - u
+ f(du/dt) = 0 for any value of the constant C
Solution
du/dt = C
Thus:
t(du/dt) - u + f(du/dt) = Ct - u + f(C) = Ct - (Ct + f(C)) + f(C)
=
Ct - Ct - f(C) + f(C) = 0
so u = Ct + f(C) satisfies the equation.

Unformatted Attachment Preview
Show that the one-parameter family of straight lines u = Ct + f(C) is a solution to the differential equation t du/dt - u + f(du/dt) = 0 for any value of the constant C Solution du/dt = C Thus: t(du/dt) - u + f(du/dt) = Ct - u + f(C) = Ct - (Ct + f(C)) + f(C) = Ct - Ct - f(C) + f(C) = 0 so u = Ct ...
Purchase document to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

### Review

Anonymous
Great content here. Definitely a returning customer.

Studypool
4.7
Indeed
4.5
Sitejabber
4.4