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Y y 0 a reduction of order with this solution

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(*) y y 0. (a) Reduction of order with this solution involves making the substitution y ve x into equation (*) and then letting w = v . Do this substitution and obtain the constant coefficient equation that w must satisfy. (b) Obtain a the general solution to the ODE that w satisfies and then stop. (c) Explain very briefly why v can be obtained from w without actually integrating. Do not attempt to actually find v. _________________________________________________________________ Silly 10 Point Bonus: Let f ( x ) = x and g ( x ) = sin( x ). (a) It is trivial to obtain a 4th order homogeneous linear constant coefficient ordinary differential equation with f and g as solutions. Do so. (b) It’s only slightly messier to obtain a 2nd order homogeneous linear ordinary differential equation with { f , g } as a fundamental set of solutions. Do so. [Say where your work is, for it won’t fit here.]
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