The general solution of y´´+ y = 0 is
c1cos(x) + c2sin(x)
(c1 + c2x)ex
c1ex + c2e−x
c1x + c2xlnx
c1x + c2lnx
Among the following differential equations, which one is exact
x2dy + 4y3dx = 0
5ydy + xdx = 0
ydx − 2xdy = 0
5sinh( y)dx + x cosh( y)dy = 0
x2ey y'+ yex = 0
Which of the following is the Laplace transform of function t2
Which of the following collections of vectors is linear dependent
(1,1,1)T , (1,1,0)T , (1,0,0)T
(1,2,4)T , (2,1,3)T , (4,−1, 2)T
(1,0,1)T , (0,1,0)T
Solve the differential equation y'' −8y'+16y = 0 , y(0) = y'(0) = 1
Let
Find all the eigenvalues and the corresponding eigenspaces
Given the basis {(1, 2,−2)T , (4,3, 2)T , (1, 2,1)T } for R3 , use the Gram-Schmidt
process to obtain an orthonormal basis.
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