How to Solve a Nonhomogeneous 2nd Order DE with a Constant Term?

Sean77771
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Homework Statement



y'' + 9y = 2x2e3x + 5

Homework Equations



N/A

The Attempt at a Solution



I think the complementary solution yc = c1cos(3x) + c2sin(3x).

If not for that little +5 at the end of the right hand side, I'm pretty sure I could solve it. But I don't know how to include it in my solution.
 
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Try adding a constant to your specific solution.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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