Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = 6x - 8y + sint y' = 4x-2y - cost Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. 134 71 O A. y(t) = C, e - + Czte -21 + 377 cost+ 377 sint 134 O B. y(t) = C, e 2ª +Czteª + 71 sint 377 cost+ 377 134 C. y(t) = C, e 2 cos 4t + C2 e 24 sin 4t + 71 377 cost+ 377 sint 134 cost+ 377 O D. y(t) = C, e - 2" cos 4t + C2 e 71 -21 sin 4t + 377 sint O E. The system is degenerate. Now find x(t) so that x(t) and the solution for y(t) found in the previous step are a general solution to the system of differential equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. X(t) =

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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.