Problem 3 (Existence and uniqueness). Consider the following initial value problems. Which of them satisfy the hypotheses of the existence and unique- ness theorem for second order equations (and therefore admit a unique solution)? In each case, justify your answer. 1. y"+Py' +y = 0 with initial conditions y(0) = 1, y'(0) = 0; %3D %3D 2. y"+Py' +y? = 0 with initial condition y(0) = 1, %3D 3. y"+ty' +y/2 = 0 with initial conditions y(0) = 1, y' (0) = 0. %3D

Problem 3 (Existence and uniqueness). Consider the following initial value problems. Which of them satisfy the hypotheses of the existence and unique- ness theorem for second order equations (and therefore admit a unique solution)? In each case, justify your answer. 1. y"+Py' +y = 0 with initial conditions y(0) = 1, y'(0) = 0; %3D %3D 2. y"+Py' +y? = 0 with initial condition y(0) = 1, %3D 3. y"+ty' +y/2 = 0 with initial conditions y(0) = 1, y' (0) = 0. %3D

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Problem 3 (Existence and uniqueness). Consider the following initial value
problems. Which of them satisfy the hypotheses of the existence and unique-
ness theorem for second order equations (and therefore admit a unique
solution)? In each case, justify your answer.
1. y" + Py' + y = 0 with initial conditions y(0) = 1, y'(0) = 0;
%3D
2. y" +ty' + y2 = 0 with initial condition y(0) = 1,
%3D
3. y"+Py' +y'/2 0 with initial conditions y(0) = 1, y'(0) = 0.

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