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#1 2008-10-09 09:26:42

C_ECE
Member
Registered: 2008-10-09
Posts: 2

1st order ODE

Hello everybody. This is my first post at this forum, and I am in need of some serious help for a question that I can't seem to figure out.

I can't solve this 1st order ODE: 3t^2 + 2t + y cos(ty) + (sin(y) + t cos(ty)) dy/dt = 0

The thing is that up until now we have learned how to solve non linear ODEs by substitution, recognizing separable equations, integrating factors, exact equations, and using Bernoulli's equation. None of these however seem to be of use for this equation, and this leaves me stumped.

Any help would be greatly appreciated,

C_ECE.

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#2 2008-10-09 09:42:34

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: 1st order ODE

The thing is that up until now we have learned how to solve non linear ODEs by substitution, recognizing separable equations, integrating factors, exact equations, and using Bernoulli's equation.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2008-10-09 11:59:33

C_ECE
Member
Registered: 2008-10-09
Posts: 2

Re: 1st order ODE

Wow I don't understand how I overlooked that, I must have not been thinking or something because I did consider that case... Thanks for the help Ricky,

C_ECE

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#4 2008-10-09 12:43:25

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: 1st order ODE

You're welcome.  My guess is that you had a numerical error when calculating the derivative to tell if it is exact or not. 

None of these however seem to be of use for this equation, and this leaves me stumped.

The one thing I never get is why students (and this is more so to my students, it doesn't apply to you all that much) never use the most important conjecture in all of mathematics:

Professors only ask you to solve problems that you should know how to solve.

From your list, the only one that is even remotely possible is exact equations.  Maybe separation, but just looking at the two cosines should give you a chill down your spine if you were to ever try to separate the variables.  In any case, using the above conjecture, you should recheck your work at least 5 times with exact equations before concluding that you don't know how to do the problem.

Even worse is my students who make a computation mistake, wind up with an impossible integral (one that they know is impossible), and then can't figure out why we would ask them to integrate it.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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