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

Integers satisfy the inequality, How many integers satisfy the inequality |...

How many integers satisfy the inequality |10(x+1)/x^2+2x+3|=1? Solution) first thing thats not an inequality, and second thing its very easy if thats the question. the LHS = |10/

Differentiate product rule functions, Differentiate following functions. ...

Differentiate following functions. Solution At this point there in fact isn't a lot of cause to use the product rule.  We will utilize the product rule.  As we add

Brad class collected 320 cans of food how many did required, Brad's class c...

Brad's class collected 320 cans of food. They boxed them in boxes of 40 cans each. How many boxes did they required? To find the number of boxes required, you should divide the

One integer is four times other what is the value of lesser, One integer is...

One integer is four times other. The sum of the integers is 5. What is the value of the lesser integer? Let x = the lesser integer and now let y = the greater integer. The ?rst

Exact differential equations, The subsequent type of first order differenti...

The subsequent type of first order differential equations which we'll be searching is correct differential equations. Before we find in the full details behind solving precise diff

Circumference of a circle, How far will a bowling ball goes in one rotation...

How far will a bowling ball goes in one rotation if the ball has a diameter of 10 inches? (π = 3.14) 1. 78.5 in 2. 31.4 in 3. 62.8 in 4. 15.7 in 2. The circumfere

Design a diagram by transformation, On a graph, design a diagram by transfo...

On a graph, design a diagram by transformation the given graph of f (x), -2 ≤ x ≤ 2. Briefly Define the other graphs in terms of f (x) and specify their domains. The diagram n

Solutions to systems, Now that we've found some of the fundamentals out of ...

Now that we've found some of the fundamentals out of the way for systems of differential equations it's time to start thinking about how to solve a system of differential equations

How many rolls will she required to purchase, Karen is buying a wallpaper b...

Karen is buying a wallpaper border for her bedroom, that is 12 ft by 13 ft If the border is sold in rolls of 5 yards each, how many rolls will she required to purchase? The dis

Find the perameter of square in maths, Find the perameter of SQUARE in math...

Find the perameter of SQUARE in maths? Remember that in a square, all sides are of equal length. A square is also a kind of rectangle. So, you can use length (l) times width

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