Find f(x) , let y = f(x) be the solution of
Solve x3 (sin x) y'''− (3x2 sin x + x3 cos x) y''+ (6x sin x + 2x2 cos x) y' − (6sin x
+2x cos x) y = 0 , given one particular solution y = x .
(1) Find the determinant and all eigenvalues of A;
(2) Find the inverse of A .
Prove in English that “The system of n linear equations in n unknowns Ax = b
has a unique solution of and only if A is nonsingular.”
(Note: No credit will be given if the answer is given in Chinese)
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