ed b eri ay,1g 10.4.5 Exercises Give the general solution of the following diffe
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ed b eri ay,1g 10.4.5 Exercises Give the general solution of the following differential equations. In each case state how many arbitrary constants you expect to find in the general solution. Are your expectations confirmed in practice solution satisfying the problem. Find the solution and check whether your expectation is confirmed. ) der dr d2x dr d'x 2 (d) 6 dx -24 de dr (c) e d' de dt For each of the following differential equation problems, state how many arbitrary constants you would expect to find in th f the HOME UOORK DONE N THE CLASExplanation / Answer
(a) Under Determined: This is a second order differenitial equation. So the general solution contains two arbitrary constants. But there is given only one condition. So all the arbitrary constants ca not be determined.
(b) Fully determined: This is a second order differential equation. So the general solution contains two arbitrary constants. To determine the arbitrary constants, we must have two conditions. There are given three conditions. Therefore, all the arbitrary constants can be determined.
The conditions are given at the boundary points 0 and 2. So this is a boundary value problem.
(c) Under determined: This is a second order differential equation. So the general solution contains two arbitrary constants. To determine the arbitrary constants, we must have two conditions. But there is given only one condition. Therefore, the arbitrary constants can not be determined.
(d) Under determined: This is a forth order differential equation. So the general solution contains four arbitrary constants. To determine the arbitrary constants, we must have four conditions. But there are given only two conditions. Therefore, all the arbitrary constants can not be determined.
(e) Fully determined: This is a second order differential equation. So the general solution contains two arbitrary constants. To determine the arbiAlso there are given two conditions. Therefore, all the arbitrary constants can be determined.
The conditions are given at the boundaries 0 and 2. So this is a boundary value problem.
(f) Fully determined: This is a second order differential equation. So the general solution contains two arbitrary constants. Also there are given two conditions. Therefore, all the arbitrary constants can be determined.
The conditions are given only at initial point 0. So this is a initial value problem.
(g) Under determined: This is a second order differential equation. So the general solution contains two arbitrary constants. To determine the arbitrary constants, we must have two conditions. But there is given only one condition. Therefore, the arbitrary constants can not be determined.
(j) Under determimed: This is a third order differential equation. So the general solution contains three arbitrary constants. But there are given only two conditios. Therefore, the arbitrary constants can not be determined.
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