Math Is Fun Forum

Old_Steve

Member

Registered: 2007-05-15

Posts: 17

Second order Diff Eq. Solved by Subsitution leading to First Order

I have a problem that I need to make subsitutions leading to first order.

x^2*y"+2*x*y'-1=0  substituting v=y' and v'=y" it becomes the first order equation x^2*v'+2*x*v-1=0

I can solve the first order via a general solution formula for a first order linear equation.  The answer for first order is v= (1/x) + (c/x^2)

I can figure out how to get back to an answer for the original second order for an answer using this required method.  I'm sure it has something to do with my rusty Calculus skills.

Can anyone figure the problem via this method?  Thanks so much!

Last edited by Old_Steve (2007-05-24 11:50:34)

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Second order Diff Eq. Solved by Subsitution leading to First Order

then

if you don't see the point of the integration, please look up formulae for integration in the Formula Section.

Last edited by George,Y (2007-05-26 03:01:02)

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X'(y-Xβ)=0

lancemaria

Member

Registered: 2007-05-22

Posts: 3

Re: Second order Diff Eq. Solved by Subsitution leading to First Order

hi

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Second order Diff Eq. Solved by Subsitution leading to First Order

hi, nice to meet you.

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X'(y-Xβ)=0

Old_Steve

Member

Registered: 2007-05-15

Posts: 17

Re: Second order Diff Eq. Solved by Subsitution leading to First Order

I see it.  Thanks George.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Second order Diff Eq. Solved by Subsitution leading to First Order

Uh, sorry, a mistake, corrected.

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X'(y-Xβ)=0