Purgatory Posted February 27, 2013 Share Posted February 27, 2013 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. Link to comment Share on other sites More sharing options...
Crimson Sunbird Posted March 1, 2013 Share Posted March 1, 2013 Your solution looks fine to me. Link to comment Share on other sites More sharing options...
x(x-y) Posted March 1, 2013 Share Posted March 1, 2013 Yeah, your answer seems to be correct - looks like an error in your textbook. Link to comment Share on other sites More sharing options...
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