2. Consider the following Differential Equation (2) y" - 2y" – 3y = cos(3r) +e. Determine the form of a particular solution by the undetermined coefficients method and write a general solution of (2). 3. Let the second order Differential Equation (3) r* y" + 2xy - 2y = 0, z € (0, x). Let yi(x) = I a first solution of (3), use the method of reduction of order to find a second solution of (3).

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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.