Question: 1. Euler-type equations. Let a, b, c be constants, and consider the following 2nd order equation with non- constant coefficients at2 . y + bt

1. Euler-type equations. Let a, b, c be constants, and consider the following 2nd order equation with non- constant coefficients at2 . y" + bt . y' + c. y = R(t). (a) Show that by introducing the substitution t = ez one may transform this equation to a 2nd order equation for (z) = y(ez) with constant coefficients. The chain rule might be useful here. (b) Use the method of part (a) to find the general solution of the equation 2 . y" - 3t . y' + 13 . y = 0 assuming t > 0

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