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4. (10%) Given the Laplace transform of Bessel function Please derive the Laplace transform of Bessel function J₀(3t).

其他申論題

2. (10%) Find the value of m, so that the given differential equation is exact. (6xy3+cosy)dx+(2mx2y2-xsiny)dy=0

3. (10%) In the following terms, which does not exist the Laplace transform?

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+...

6. (10%) Find the serial solutions at x=0 for the following differential equation. x(x-1)y"+(3x-l)y'+y=0

7. (10%) For Legendre's different equation (1-x2)y"-2xy'+λy =0 in which -1≤x≤1, and 2 is a real constant, please find the serial solutions at x=0 and explain how to get the Legendre's polynomials.

8. (10%) Find fit) from the following equation.

9. (10%) Solve the following equation(10%)

1. Worüber hat der Autor gelesen?

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