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Dave321
 3 years ago
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?
Dave321
 3 years ago
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?

This Question is Closed

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

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

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

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

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

abtrehearn
 3 years ago
Best 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.

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

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

abtrehearn
 3 years ago
Best ResponseYou've already chosen the best response.1For 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.

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

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

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