1. Confirm that the equation is linear, then determine (without solving) an interval in which of the given initial value problem is certain to exist. (Use Theorem 1, given below.) (a) y +(tant)y = sin t, y(7) = 0 %3D

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1. Confirm that the equation is linear, then determine (without solving) an interval in which the solution
of the given initial value problem is certain to exist. (Use Theorem 1, given below.)
(a) y+ (tant)y = sin t, y(n) 0
Transcribed Image Text:1. Confirm that the equation is linear, then determine (without solving) an interval in which the solution of the given initial value problem is certain to exist. (Use Theorem 1, given below.) (a) y+ (tant)y = sin t, y(n) 0
Theorem 1. If the functions p and g are continuous on the open interval I: a <t<B containing the
point t to, then there exists a unique function y (t) that satisfies the differential equation
%3D
y +p(t) y = 9(t)
for each t in I, and that also satisfies the initial condition
y(to) = yo,
%3D
where yo is an arbitrary prescribed initial value.
Transcribed Image Text:Theorem 1. If the functions p and g are continuous on the open interval I: a <t<B containing the point t to, then there exists a unique function y (t) that satisfies the differential equation %3D y +p(t) y = 9(t) for each t in I, and that also satisfies the initial condition y(to) = yo, %3D where yo is an arbitrary prescribed initial value.
Expert Solution
Step 1

A first order linear ordinary differential equation has the form of y’(x) + p(x) y = q(x)

 

The linear differential equation is of the form:

a0xy+a1xy'+a2xy''++anxyn+bx=0where a0x,a1x,,anxand bx are arbitrary differentiable function.

The equation is in first order linear ordinary differential equation form.

 

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