Solve y'= (4x2 + y2 ) / xy .
Solve by substitution: xy'+ y = x2 y2 , y(1) = 1/ 3 .
Solve y''+ 9y = 27x + (cos3x) / 5 .
Evaluate the following problems:
Find the Fourier series of the given function f(x) , which is assumed to have the
period 2π , where f(x) = 0 if −π < x < 0 , f(x) = 1 if 0 < x <π .
(1) Find the inverse of [A] .
(2) Find all the eigenvalues and their corresponding cigenvectors of [B] .
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