Finding Particular Solutions for Second Order Linear Differential Equations

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Homework Statement



Find particular solution for
y''+2y'+5y = 4(e^-t)cos2t

Homework Equations



y.c = C(e^-t)cos2t + C(e^-t)sin2t

The Attempt at a Solution



y.p (particular solution) = At(e^-t)cos2t + Bt(e^-t)sin2t does not work! Help please!
 
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Are you sure your y_p doesn't work? Why don't you show us what you're getting when you plug it into the ODE.
 
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reply oh i figured it out. thank you!
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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