Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x' + y' - 4x -бу —D е -t x' +y' + 8x + 3y = et B. x(t) = C, cos (6t) + C, sin (6t) + 2 -t e + 37 37 O C. x(t) = C, e 6t cos (6t) + C, e 6t sin (6t) + e 37 37 O D. X(t) = C, cos (6t) + C, sin (6t) Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of differential equations. y(t) = |

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Q: (9) Solve the following diserental equation dy dx 2 3+y 3.x 3-y = (9x - y²x), y(0) = 0 Answer: = e

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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.