Verify that the vector X is a solution of the given homogeneous linear system. dx = -2x + 5y dt 5 cos(t) 3 cos(t) – sin(t) dy = -2x + 4y; dt X = Writing the system in the form X' = AX for some coefficient matrix A, one obtains the following. X' = 5 cos(t) ( 3 cos(t) – sin(t), For e', one has X' = AX =

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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.