Solve the following differential equations.
(1) −3ydx + 4xdy = 0
(2) 8y''(x) − 6y'(x) + 6y(x) = 0
(3) x2y''(x) + 6xy'(x) + 6y(x) = 0
Find the Laplace transforms of the following functions.
(1) t2cost
(2) (t3 − 2)2
Find the Inverse Laplace transforms of the following functions.
The Laguerre differential equation is xy''+ (1− x) y' +λy = 0 .
(1) Show that x = 0 is a regular singular point.
(2) Determine the indicial equation, its roots, the recurrence relations and one solution
(x > 0) .
(3) Shows that if λ = m , a positive integer, this solution will reduce to a polynomial.
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