Theorem of reduction of order, Mathematics

Assignment Help:

In this theorem we identify that for a specified differential equation a set of fundamental solutions will exist.

Consider the differential equation

 y′′ + p (t ) y′ + q (t ) y = 0

 Here p(t) and q(t) are continuous functions on any interval I. select t0 to be any point in the interval I. Let y1(t) be a solution to the differential equation which satisfies the initial conditions.

 y(t0) = 1

 y′ (t0) = 0

 Let y2(t) be a solution to the differential equation which satisfies the initial conditions.

 y (t0) = 0

 y′ (t0) = 1

 So y1(t) and y2(t) form a fundamental set of solutions for the differential equation.

This is easy enough to illustrate that these two solutions form a fundamental set of solutions. Just calculate the Wronskian.

976_THEOREM of Reduction of Order.png

Thus, fundamental sets of solutions will exist; we can solve the two IVP's specified in the theorem.


Related Discussions:- Theorem of reduction of order

Mutually exclusive events, Mutually Exclusive Events A set of events i...

Mutually Exclusive Events A set of events is said to be mutually exclusive if the occurrence of any one of the events precludes the occurrence of any of the other events for i

Setup the mass balance equation - linear system method, Two tanks initially...

Two tanks initially contain 100 liter liquid each. Their initial concentration are listed in the Figure below. At time zero, the input and output valves are opened simultaneously w

Analysis of algorithm running time - undirected graph, Problem. You are giv...

Problem. You are given an undirected graph G = (V,E) in which the edge weights are highly restricted. In particular, each edge has a positive integer weight of either {1, 2, . .

Facts regarding linear equations, To solve out linear equations we will mak...

To solve out linear equations we will make heavy use of the following facts. 1. If a = b then a + c = b + c for any c.  All it is saying that we can add number, c, to both sides

Area between curves, Area between Curves In this section we will be fi...

Area between Curves In this section we will be finding the area between two curves. There are in fact two cases that we are going to be looking at. In the first case we des

How long will it take her to save $350, Each week Jaime saves $25. How long...

Each week Jaime saves $25. How long will it take her to save $350? Divide $350 by $25; 350 ÷ 25 = 14 weeks.

Mathematical statements are unambiguous- nature of math, Mathematical State...

Mathematical Statements Are Unambiguous :  Consider any mathematical concept that you're familiar with, say, a sphere. The definition of a sphere is clear and precise. Given any o

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd