# Find a solution to d^(2y)/dt^2 =-4y

Find a solution to ${d}^{2y}/d{t}^{2}=-4y$
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jbacapzh
${d}^{2y}/d{t}^{2}=-4y$
$⇒{d}^{2y}/d{t}^{2}+y=0$
this is homogeneous DE
the characteristic equation is:
${m}^{2}+1=0$
$m=±i$
the general solution is:
$y={c}_{1}{e}^{-ix}+{c}_{2}{e}^{ix}$
or
$y={c}_{1}\mathrm{cos}x+{c}_{2}\mathrm{sin}x$
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Ashlyn Krause
Find a solution to ${d}^{2y}/d{t}^{2}=-4y$
y''-4y=0
${m}^{2}-4=0$
$m=±2$
$y={c}_{1}\mathrm{exp}\left(m1t\right)+{c}_{2}\mathrm{exp}\left(m2t\right)$
$y={c}_{1}\mathrm{exp}\left(-2t\right)+{c}_{2}\mathrm{exp}\left(2t\right)$