- #1

karush

Gold Member

MHB

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Find the general solution of the given differential equation, and use it to determine how solutions behave as $ t\to\infty$ $y'+y=5\sin{2t}$

ok I did this first

$u(t)y'+u(t)y=u(i)5\sin{2t}$

then

$\frac{1}{5}u(t)y'+\frac{1}{5}u(t)y=u(i)\sin{2t}$

so far ... couldn't find an esample to follow

____________________________________________

book answer

$y=ce^{−t}+\sin 2t−2\cos 2t$

$\textit{y is asymptotic to sin2t−2cos2t as $t\to\infty$}$

ok I did this first

$u(t)y'+u(t)y=u(i)5\sin{2t}$

then

$\frac{1}{5}u(t)y'+\frac{1}{5}u(t)y=u(i)\sin{2t}$

so far ... couldn't find an esample to follow

____________________________________________

book answer

$y=ce^{−t}+\sin 2t−2\cos 2t$

$\textit{y is asymptotic to sin2t−2cos2t as $t\to\infty$}$

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