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Linear First order differentials


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Hi.

 

I am struggling to understand what I am doing wrong with this equation.

 

They ask for the general solution and then the particular solution afterwards.

 

Given

x(dy/dx) + 5y = 7x^2 , y(2)=5

 

=> dy/dx + (5/x)y = 7x

 

integrating factor: e^integral(5/x) = e^(5lnx) = x^5

 

multiply by this gives: x^5(dy/dx)+(5/x)y(x^5)= 7x^6

 

=> Dx[(x^5)(y)]= 7x^6

 

integrate both sides

=> (x^5)(y)= x^7 + C

 

=> y(x)= x^2 + C/(x^5) (divided by x^5)

ok thats the general solution

 

Now I get the particular solution by subin in (2,5)

 

so 5 = 4 + C/32

 

so C = 32 sub in and you have an answer...

 

The answer they give is y(x)= (x+4x^-2)

It makes no sense in my head.. If anyone could confirm my answer it would be appreciated.

 

 

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