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Solving Second Order Diffy Q: Find k & Verify Solutions
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[QUOTE="UltrafastPED, post: 4547780, member: 486686"] If k=+5/2 is a solution (test it!), and k=-5/2 is a solution (test it!), then you have two solutions: cos(5/2t) and cos(-5/2t). You should also check for sin(5/2t), sin(-5/2t). but if u is a solution, and v is a solution, then so is Au + Bv ... 2nd order ODE has two independent solutions, and their sum (multiplied by arbitrary constants A,B) is the general solution for the homogeneous case. So the general process for an ODE of order n is to find n independent solutions, then multiply each by an arbitrary constant, and sum them all up ... that is the general solution ... you can then apply the boundary conditions provided which will determine the values of A,B, ... for that case. There is actually a theory which describes all of this which you will study if you take an advanced course in differential equations - but in the introduction the goal is to learn how to solve them. [/QUOTE]
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Solving Second Order Diffy Q: Find k & Verify Solutions
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