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Linear First order differentials

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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.



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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