Reba is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $8, and her grandmother has pledged $2 p
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Recall that variation of parameters is used to solve second-order ODEs of the form
<em>y''(t)</em> + <em>p(t)</em> <em>y'(t)</em> + <em>q(t)</em> <em>y(t)</em> = <em>f(t)</em>
so the first thing you need to do is divide both sides of your equation by <em>t</em> :
<em>y''</em> + (2<em>t</em> - 1)/<em>t</em> <em>y'</em> - 2/<em>t</em> <em>y</em> = 7<em>t</em>
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You're looking for a solution of the form
where
and <em>W</em> denotes the Wronskian determinant.
Compute the Wronskian:
Then
The general solution to the ODE is
which simplifies somewhat to
Domain of 
are the values of x for which 2x + 1 < 0
2x < -1
x < -1/2
Therefore, domain is all real numbers less than -1/2
2x < -1
x < -1/2
Therefore, domain is all real numbers less than -1/2