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We define the linear DE for x > 0:
x2y" + axy' + by = 0.
Use the substitution u = ln(x) to transform the equation to the constant-coefficient equation of the form
d2y/du2 + (a - 1) dy/du + by = 0
a. Find a and b.
b. Solve the constant-coefficient equation in u to find two linearly independent solution.
c. Use part (b) to find solution of the DE when a = 1 and b = -1/2. FInd the solution when y(1) = 0 and y'(1) = 1.
How many bacteria in the original solution?
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