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Dave321
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Solve dy/dx=(5x+y)^2 4
I got 1/6ln((u3)/(u+3))=x using a substitution of u=(5x+y). Is that right?
 3 years ago
 3 years ago
Dave321 Group Title
Solve dy/dx=(5x+y)^2 4 I got 1/6ln((u3)/(u+3))=x using a substitution of u=(5x+y). Is that right?
 3 years ago
 3 years ago

This Question is Closed

bward10 Group TitleBest ResponseYou've already chosen the best response.0
the problem isnt stated properly... it looks wrong though. some clarification would help.
 3 years ago

Dave321 Group TitleBest ResponseYou've already chosen the best response.1
What do you mean?
 3 years ago

Dave321 Group TitleBest ResponseYou've already chosen the best response.1
\[dy/dx=(5x+y)^24\] Is that better?
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
That usubstitution works for this differential equation. The substitution reduces it to the variablesseparable equation \[du/(u^{2}9) + dx = 0.\]
 3 years ago

Dave321 Group TitleBest ResponseYou've already chosen the best response.1
But then you still have to integrate it, right?
 3 years ago

Dave321 Group TitleBest ResponseYou've already chosen the best response.1
Did you get the same answer I got?
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
Computing ...
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
(1/6)(lnu  3  lnu + 3 = x + ln(C)/6 as an intermediate solution. Once that is taken back to original variables, we're finished.
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
My final solution is 5x  y + 3 = C e^(6x)(5x  y  3) in implicit form.
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
Its explicit form is \[y = 5 x + 3(1 + C e^{6x})/(1 + C e^{6x}).\]
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
For increasingly large values of x, all solution curves more closely approximate the linear function 5x + 3, so the line y = 5x + 3 is the asymtote of all solution curves.
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
That's a good problem, Dave :^)
 3 years ago

Dave321 Group TitleBest ResponseYou've already chosen the best response.1
I'll tell my professor;) Thanks!
 3 years ago

abtrehearn Group TitleBest ResponseYou've already chosen the best response.1
Major tenfour, good buddy :^)
 3 years ago
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