[2 2] 3 1 X' = X+ Find a fundamental matrix 4(t) for the associated homogeneous system. Also, determine the vector u (t) satisfying the equation X(t) = 4(t) u (t) which is a particular solution of the nonhomogeneous system. Teft -2et e-6t 15 OA. 4(t) = ett ;u (t) = 3et 1 est 25 e4t 2et B. U(t) = e4t -3et 1 (t) = est 1 t - 15 e4t 2et O C. 4(t) =| e4t (t) = -3et 1 25 t+ e-6t e4t -2e* O D. 4(t) = (t) eft 3et eSt 25

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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.