Distinct roots, Mathematics

Assignment Help:

There actually isn't a whole lot to do throughout this case.  We'll find two solutions which will form a basic set of solutions and therefore our general solution will be as,

2065_Distinct Roots.png

Example: Solve the following initial value problem

2 x2 y′′ + 3xy′ -15 y = 0,

 y (1) = 0

 y′ (1) = 1

 Solution

We first require finding the roots to (3).

2r ( r -1) + 3r -15 = 0

2r2 + r -15 = (2r - 5)(r + 3) = 0

⇒         r1 = 5/2 and                          r2 = -3

Then the general solution is,

y(x) = c1x5/2 + c2 x-3

To get the constants we differentiate and plug into the initial conditions where we did back into the second order differential equations section.

y'(x) = (5/2) c1x3/2 - 3c2 x-4

0 = y(1) = c1 + c2

1 = y'(1) = (5/2)c1 + (-3) c2

By solving these equations we get:

c1 = 2/11,

c2 = -(2/11)

the actual solution is,

y(x) = (2/11) x5/2  -(2/11) c2 x-3


Related Discussions:- Distinct roots

Determination of the regression equation, Determination of the Regression E...

Determination of the Regression Equation The determination of the regression equation such given above is generally done by using a technique termed as "the method of least sq

Explain mixed numbers with examples, Explain Mixed Numbers with examples? ...

Explain Mixed Numbers with examples? Everybody loves a bargain, right? But sometimes these "special deals" aren't what they seem to be. For example, pretend you were at a

Debate over answer to an equation..., The math equation is written exactly ...

The math equation is written exactly this way: 0+50x1-60-60x0+10=??? The answer I get is 10 and others say 0 0+50=50 50x1=50 50-60=-10 -10-60=-70 -70x0=0 0+10=10

Congruence of triangle, make an assignment based on congruence of triangle

make an assignment based on congruence of triangle

Two tailed tests, Two Tailed Tests A two tailed test is generally used ...

Two Tailed Tests A two tailed test is generally used in statistical work as tests of significance for illustration, if a complaint lodged by the client is about a product not m

Matrix, how to solve for x

how to solve for x

Prove that 2b3-3abc+a2d=0, If  the  ratios  of  the  polynomial ax 3 +3bx...

If  the  ratios  of  the  polynomial ax 3 +3bx 2 +3cx+d  are  in  AP,  Prove  that  2b 3 -3abc+a 2 d=0 Ans: Let p(x) = ax 3 + 3bx 2 + 3cx + d and α , β , r are their three Z

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