Question

Annihilator Method) applies to any nonhomogeneous term as long as the associated homogeneous equation has constant coefficients. 6. Variation of parameters works for all differential equations. In Problems 7-11, consider the particular solutions of their respective forced equations $P(D)(y) = F_1(x)$ and $P(D)(y) = F_2(x)$. Find a particular solution for the new forcing function in $P(D)(y) = F_3$. 7. $y'' + y' - 6y = 50$ with $y_p = -\frac{25}{3}$ and $y'' + y' - 6y = 36x$ with $y_p = -6x - 1$; $F_2(x) = 100 - 18x$ 8. $y'' + 2y' + 6y = 2$ with $y_p = \frac{1}{3}$ and $y'' + 2y' + 6y = e^x$ with $y_p = \frac{1}{9}e^x$; $F_2(x) = 6 + 9e^x$

          Annihilator Method) applies to any nonhomogeneous term as long as the
associated homogeneous equation has constant coefficients.
6. Variation of parameters works for all differential equations.
In Problems 7-11, consider the particular solutions of their respective forced
equations $P(D)(y) = F_1(x)$ and $P(D)(y) = F_2(x)$. Find a particular solution
for the new forcing function in $P(D)(y) = F_3$.
7. $y'' + y' - 6y = 50$ with $y_p = -\frac{25}{3}$ and $y'' + y' - 6y = 36x$ with $y_p = -6x - 1$;
$F_2(x) = 100 - 18x$
8. $y'' + 2y' + 6y = 2$ with $y_p = \frac{1}{3}$ and $y'' + 2y' + 6y = e^x$ with $y_p = \frac{1}{9}e^x$;
$F_2(x) = 6 + 9e^x$

Annihilator Method) applies to any nonhomogeneous term as long as the
associated homogeneous equation has constant coefficients.
6. Variation of parameters works for all differential equations.
In Problems 7-11, consider the particular solutions of their respective forced
equations P(D)(y) = F1(x) and P(D)(y) = F2(x). Find a particular solution
for the new forcing function in P(D)(y) = F3.
7. y” + y' - 6y = 50 with yp = -(25)/(3) and y” + y' - 6y = 36x with yp = -6x - 1;
F2(x) = 100 - 18x
8. y” + 2y' + 6y = 2 with yp = (1)/(3) and y” + 2y' + 6y = e^x with yp = (1)/(9)e^x;
F2(x) = 6 + 9e^x

Added by Anthony R.

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