1. Confirm that the equation is linear, then determine (without solving) an interval in which the solutionof 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

Answered: 1. Confirm that the equation is linear,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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.

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:

$a_{0} (x) y + a_{1} (x) y^{'} + a_{2} (x) y^{''} + \dots + a_{n} (x) y^{n} + b (x) = 0 where a_{0} (x), a_{1} (x), \dots, a_{n} (x) and b (x) are arbitrary differentiable function.$

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

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