Find a particular solution y, of the following equation. Primes denote the derivatives with respect to x. y(5) + 2y) +2y" = 8x² - 9 The particular solution is y, (x) =.

Verify the formula by differentiation. S5 The 5 5x+8 8 dx = In |5x + 8 + C, x# - 5 can be used to verify the given formula.

7. Mira is a red giant star estimated to be 200-400 light years from the sun in the constellation of Cetus. Today we know this star varies in brightness. The brightness of the star, B, over time can be modeled by the equation B(t) 2 sin 8. -t) +6. where t represents time, in months. Mira's last brightness peak was in February of 2021. Determine what month and year Mira will experience its next brightness peak. •BIUS x, x 9 A- A- Q V Format Font Size T.

II Find the general solution to the equation Ut + xUx = sin t.