# Note that both of the solutions blow up as t 0 but

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Note that both of the solutions blow up as t 0, but this is not unexpected because when it is written in the standard form for linear differential equations, d 2 x dt 2 + 6 t dx dt + 6 t 2 x = 0 , its coefficients P ( t ) = 6 t and Q ( t ) = 6 t 2 blow up as t 0.

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4. The differential equation t 2 d 2 x dt 2 - 4 t dx dt + 6 x = 0 has the general solution a. x = c 1 t + c 2 t 2 b. x = c 1 t 2 + c 2 t 3 c. x = c 1 (1 /t ) + c 2 (1 /t 2 ) d. x = c 1 (1 /t 2 ) + c 2 (1 /t 3 ) e. None of these Hint: Try solutions of the form x = t λ . Correct answer: b

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