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anonymous
 5 years ago
show that the oneparameter family of straight lines u = Ct + f(C) is a solution to the diff. eq. tu'  u  f(u') = 0 for any value of the constant C.
anonymous
 5 years ago
show that the oneparameter family of straight lines u = Ct + f(C) is a solution to the diff. eq. tu'  u  f(u') = 0 for any value of the constant C.

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watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0\(tu'uf(u')=tC(Ct+f(C))+f(C)=0\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what is the reasoning behind this?

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0For \(u=Ct+f(C)\) we have \(u'=C\) and you just plug in \(u\) and \(u'\) into the equation and verify that it is equal to zero.
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