Consider the following second-order, linear, homogeneous equations, and their solutions where x > 0. Determine if y1 and y2 form a fundamental set of solutions. If they do develop a relation for y(x) that contains all solutions of the differential equations? y^''-2y^'+3y=0; y_1=e^x sin⁡〖√2 x〗 and y_2=e^x cos⁡〖√2 x〗

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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.