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

Calculus, Properties of Integration

Properties of Integration

Dividing fractions by fractions with drawing.., how do I divide a fraction ...

how do I divide a fraction by a fraction by drawing a picture

Calculate the probability - contingency table, 1) A survey was done where a...

1) A survey was done where a random sample of people 18 and over were asked if they preferred comedies, dramas, or neither. The information gathered was broken down by age group an

Children learn maths by experiencing things, Children Learn By Experiencing...

Children Learn By Experiencing Things : One view about learning says that children construct knowledge by acting upon things. They pick up things, throw them, break them, join the

Describe the introduction to integers, Describe the Introduction to Integer...

Describe the Introduction to Integers ? Integers include the positive and negative whole numbers, such as -4, -3, -2, -1, 0, 1, 2, 3, 4, and so on. A negative number has a "

Describe visualize solutions of simultaneous equations, Describe Visualize ...

Describe Visualize Solutions of Simultaneous Equations ? By drawing the graph of each equation in a system of equations, you can see a picture of the system's solutions. Fo

Ampltude and period, find the amplitude and period of y=3 sin 2 pi x

find the amplitude and period of y=3 sin 2 pi x

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