Differential Equations | Part IA, 2005

Obtain the general solution of

x2d2ydx2+xdydx+y=0x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y=0

by using the indicial equation.

Introduce z=logxz=\log x as a new independent variable and find an equivalent second order differential equation with constant coefficients. Determine the general solution of this new equation, and show that it is equivalent to the general solution of ()(*) found previously.

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