(1 point) Given the IVP Fundamental Existence Theorem for Linear Differential Equations dy an(x). da d-ly dan-1 +an-1(2)

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1 Point Given The Ivp Fundamental Existence Theorem For Linear Differential Equations Dy An X Da D Ly Dan 1 An 1 2 1 (48.54 KiB) Viewed 12 times

(1 point) Given the IVP Fundamental Existence Theorem for Linear Differential Equations dy an(x). da d-ly dan-1 +an-1(2)- y(ro) = yo, y' (zo) = dy da +...+a₁(x). =y, + a(z)y= g(x) yn 1) (20)=Yn-1 (n-1), If the coefficients a, (z),..., a(z) and the right hand side of the equation g(x) are continuous on an interval I and if a(z) 0 on I then the IVP has a unique solution for the point zo € I that exists on the whole interval I It is useful to introduce an operator notation for derivatives. In particular we set D differential equation above as. d da which allows us to write the (an(x)D(n) + an-1(2) D(n-1) +...+ a₁(z)D + a₁(x)) y = g(x) A note about putting in your answers. Some problems have may have answer blanks that require you to enter an intervals. Intervals can be written using interval notation: (2, 3) is the numbers z with 2<x<3 while (2,3] is the interval 2 <r <3. If you want oo type inf, for example for the interval (-∞, oo) you would type: