[tex]w[f,g](t)= t^2\exp{t}\\f(t)=t[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Thats what i get, the problem is to find g(t)

So, i start; f'(t)=1

[tex]w[f,g](t)= t^2\exp{t}=f(t)g'(t)-f'(t)g(t)\\t^2\exp{t}=tg'(t)-g(t)[/tex]

divide by t,

[tex]t\exp{t}=g'(t)-\frac{g(t)}{t}[/tex]

its a 1st order linear eq. I solve for the integrating factor and get t. i multiply through and reduce

[tex](tg(t))'=t^2\exp{t}[/tex]

then i integrate with the product rule and get

[tex]tg(t)=t^2\exp{t}+2t\exp{t}+C[/tex]

divide by t and get

[tex]g(t)=t\exp{t}+2\exp{t}+\frac{C}{t}[/tex]

which is wrong. The answer in the book is

[tex}t\exp{t}+Ct[/tex]

not sure where i went wrong, i know its probably something dumb, but its late, so i need help.

~gale~

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# Wronskian problem

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