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110年 - 成大_資訊聯招_工程數學#105389
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題組內容
1. (20%) Solve the given differential equation.
(a)
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(b)
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2. (10%) Find the value of m, so that the given differential equation is exact. (6xy3+cosy)dx+(2mx2y2-xsiny)dy=0
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3. (10%) In the following terms, which does not exist the Laplace transform?
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4. (10%) Given the Laplace transform of Bessel function Please derive the Laplace transform of Bessel function J0(3t).
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5. (10%) Please find the indicial equation of the following differential equation. y"+p(x)y'+q(x)y=0, x = 0 is a regular sigular point. where xp(x) = A0 + A1x+A2x2+... x2g(x)= B0 +B1x+B2x2+...
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6. (10%) Find the serial solutions at x=0 for the following differential equation. x(x-1)y"+(3x-l)y'+y=0
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