Answer 6b. Suppose that the coefficient functions p(t) and q(t) are continuous in the interval (0,π), and the functions ?1(?) = ?, ?2(?) = ???? are solutions of the ODE 6. Suppose that the coefficient functions p(t) and q(t) are continuous in the interval (0, x),and the functions y, (t) = t, y2(t) = sint are solutions of the ODEy" + p(t)y' +q(t)y=00

The given ODE is - y'' + p(t)y' + q(t)y = 0, 0<t<π The given functions which are solutions…

Answered: Answer 6b. Suppose that the coefficient…

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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Answer 6b. Suppose that the coefficient functions p(t) and q(t) are continuous in the interval (0,π), and the functions ?1(?) = ?, ?2(?) = ???? are solutions of the ODE

6. Suppose that the coefficient functions p(t) and q(t) are continuous in the interval (0, x),
and the functions y, (t) = t, y2(t) = sint are solutions of the ODE
y" + p(t)y' +q(t)y=0
0 <t < n
a) Compute the Wronskian of y, y2. Are they linearly independent on the interval
(0, n)
b) Is the pair {y, Y2} fundamental set of solutions for the ODE?
c) Find the solutions y(t) of the initial value problem for the ODE with initial conditions
y(T/2) = 0, y'(/2) = 2

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