Differential equation - variation of parameters, Mathematics

Assignment Help:

Variation of Parameters

Notice there the differential equation,

y′′ + q (t) y′ + r (t) y = g (t)

Suppose that y1(t) and y2(t) are a fundamental set of solutions for

y′′ + q (t ) y′ + r (t ) y = 0

888_Differential equation - Variation of Parameters1.png

Depending on the problem and the person, some will determine the formula easier to notice and use, whereas others will determine the process used to find the formula easier.  The illustrations in this section will be done using the formula.

 Before proceeding along with a couple of illustrations let's first address the issues including the constants of integration which will arise out of the integrals. Placing in the constants of integration will provide the following.

1823_Differential equation - Variation of Parameters.png

The last quantity in the parenthesis is nothing more than the complementary solution along with c1 = - c and c2 = k and we identify that if we plug this in the differential equation this will simplify out to zero as this is the solution to the homogeneous differential equation. Conversely, these terms add nothing to the particular solution and thus we will go ahead and suppose that c = 0 and k = 0 in all the illustrations.

One last note before we proceed along with illustrations.  Do not worry about that of your two solutions in the complementary solution is y1(t) and that one is  y2(t). This doesn't matter. You will finds out the same answer no matter that one you select to be y1(t) and which one you choose to be y2(t).


Related Discussions:- Differential equation - variation of parameters

How to creates factor by substitution, How to creates Factor by Substitutio...

How to creates Factor by Substitution ? Can you factor this polynomial? x 2 + 3x + 2 (For this tutorial, I'm going to assume that you know how to do some basic factorin

Decision-making under conditions of certainty, Decision-Making Under Condit...

Decision-Making Under Conditions of Certainty Conditions of certainty tend to be rare, especially when significant decisions are involved. Under conditions of certainty, decis

#title, how do you do hard math!!!

how do you do hard math!!!

Permatuation and combination problem, 4 boys and 4 girls are to seated in a...

4 boys and 4 girls are to seated in arow i)no. of girls sit together ii)not all girls sit together iii)boys and girls are altenate to each other iv)if a particular boy and g

Find the area of the shaded region of square, In the adjoining figure, ABCD...

In the adjoining figure, ABCD is a square of side 6cm.  Find the area of the shaded region. Ans:    From P draw PQ ⊥ AB AQ = QB = 3cm (Ans: 34.428 sq cm) Join PB

Determine the mass of the hemisphere, Question 1. Use cylindrical coordinat...

Question 1. Use cylindrical coordinates to nd the mass of the solid of density e z which lies in the closed region  Question 2. The density of a hemisphere of radius a (y 

Show that 8 - 10 + 21= 0, If A, B and P are the points (-4, 3), (0, -2) and...

If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans :   AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2

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