Question

(1 point) Match the following guess solutions $y_p$ for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below.\\ A. $y_p(x) = Ax^2 + Bx + C$, B. $y_p(x) = Ae^{2x}$, C. $y_p(x) = A \cos 2x + B \sin 2x$,\\D. $y_p(x) = (Ax + B) \cos 2x + (Cx + D) \sin 2x$ E. $y_p(x) = Axe^{2x}$, and F. $y_p(x) = e^{3x}(A \cos 2x + B \sin 2x)$\\ 1. $\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = e^{2x}$\\ 2. $\frac{d^2y}{dx^2} + 4y = -3x^2 + 2x + 3$\\ 3. $y'' + 4y' + 13y = 3 \cos 2x$\\ 4. $y'' - 2y' - 15y = e^{3x} \cos 2x$

          (1 point) Match the following guess solutions $y_p$ for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below.\\
A. $y_p(x) = Ax^2 + Bx + C$, B. $y_p(x) = Ae^{2x}$, C. $y_p(x) = A \cos 2x + B \sin 2x$,\\D. $y_p(x) = (Ax + B) \cos 2x + (Cx + D) \sin 2x$ E. $y_p(x) = Axe^{2x}$, and F. $y_p(x) = e^{3x}(A \cos 2x + B \sin 2x)$\\
1.  $\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = e^{2x}$\\
2.  $\frac{d^2y}{dx^2} + 4y = -3x^2 + 2x + 3$\\
3.  $y'' + 4y' + 13y = 3 \cos 2x$\\
4.  $y'' - 2y' - 15y = e^{3x} \cos 2x$

(1 point) Match the following guess solutions yp for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below.

A. yp(x) = Ax^2 + Bx + C, B. yp(x) = Ae^2x, C. yp(x) = A cos 2x + B sin 2x,
D. yp(x) = (Ax + B) cos 2x + (Cx + D) sin 2x E. yp(x) = Axe^2x, and F. yp(x) = e^3x(A cos 2x + B sin 2x)

1. (d^2y)/(dx^2) - 5(dy)/(dx) + 6y = e^2x

2. (d^2y)/(dx^2) + 4y = -3x^2 + 2x + 3

3. y” + 4y' + 13y = 3 cos 2x

4. y” - 2y' - 15y = e^3xcos 2x

Added by Joaquin K.

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