Match the following guess solutions y, for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below. A. Yp(x) = Az² + Bx + C, B. Y,(x) = Ae2" c. y,(r) = A cos 2x + Bsin 2x, D. yp(x) = (Ax + B) cos 2x + (Cr + D) sin 2x E. y,(r) = Are, and F. y,(æ) = e(A cos 2r +B sin 2r) d?y 1. + 4y = x – 20 dx? d'y + 6 dx 2. + 8y = e2 dr? 3. y" + 4y' + 13y 3 cos 2x 4. y" – 2y'- 15y = 3x cos 2x

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.