Problems For problems 14-15, find L 1 L 2 and L 2 L 1 for the given differential operators, and determine whether L 1 L 2 = L 2 L 1 . L 1 = D + 1 , L 2 = D − 2 x 2
Problems For problems 14-15, find L 1 L 2 and L 2 L 1 for the given differential operators, and determine whether L 1 L 2 = L 2 L 1 . L 1 = D + 1 , L 2 = D − 2 x 2
Solution Summary: The author explains that the linear differential operator of order n is given by, L=Dn+a_1
in this problems find a linear differential operator that annihilates the given function.
typed answer needed
If
find az/au and az/av.
?z/?u
Əz/dv =
z = sin(x² + y²),
x = u cos(v),
y = u sin(v),
REMARK. This problem is unusual: the system expects simplified answers. For example, if the correct answer is a function of u and v identically equal to 1, then
the expression exp(uv) *exp(-uv) would not be accepted, while the constant 1 would be.
HINT. Try to simplify the *function* itself before differentiating it.
Find the general solutions to the following difference and differential equatic
(3.1) Un+1=un +7
(3.2) Un+1=u8,0 = 2
(3.3)=3tP5 - p5
(3.4)=3-P+3t - Pt
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