Given
eigenvectors associated with distinct eigenvalues are orthogonal.
Find the eigenvalues, eigenvectors and Jordan-canonical-form representation of the
Consider the following differential equations:
(1) Find the general solutions
(2) Find the solutions if the initial conditions are x1(0) = 2 , x2(0) = −7 .
Solve the initial value problem of x2y''− xy'= 0 ; y(2) = 5 , y'(2) = 8 .
Find the general solution of y''− 6y'+ 9y = 5e3x .
(1) Find 4 solutions of the following differential equation and prove that they are
linear independent:
(2) What is the general solution of the differential equation?
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