Find a general solution to the differential equation, Mathematics

Assignment Help:

Example: Find a general solution to the subsequent differential equation.

2 y′′ + 18 y + 6 tan (3t)

Solution

First, as the formula for variation of parameters needs coefficients of a one in front of the second derivative let's support that before we not remember. The differential equation which we'll in fact be solving is

y′′ + 9 y + 3 tan (3t)

We'll leave this to you to verify as the complementary solution for that differential equation is,

yc (t ) = c1 cos (3t)+ c2 sin (3t)

 Therefore, we have

 y1 (t) = cos (3t)

 y2 (t) = sin (3t)

 The Wronskian of these two functions is

833_Find a general solution to the subsequent differential equation.png

= 3cos2(3t) + 3sin2(3t) = 3

The particular solution is after that,

2387_Find a general solution to the subsequent differential equation1.png

The general solution is,

y (t ) = c1 cos (3t ) + c2 sin(3t) In |sec(3t) + tan (3t)|


Related Discussions:- Find a general solution to the differential equation

Arc length formula - applications of integrals, Arc length Formula L = ...

Arc length Formula L = ∫ ds Where ds √ (1+ (dy/dx) 2 ) dx                                     if y = f(x), a x b ds √ (1+ (dx/dy) 2 ) dy

Problem solving, if you start a business and john creates 6 t shirts more t...

if you start a business and john creates 6 t shirts more than pedro and pedro four t shirts less than eva and between the three of then made 22 tshirts, how many t-shirts made each

Sqrt n- sqrt 8836, How many integers satisfy (sqrt n- sqrt 8836)^2 Solutio...

How many integers satisfy (sqrt n- sqrt 8836)^2 Solution) sqrt 8836 = 94 , let sqrt n=x the equation becomes... (x-94)^2 (x-94)^2 - 1 (x-95)(x-93) hence  93 8649  the number o

6th grade, what is the length of a line segment with endpoints (-3,2) and (...

what is the length of a line segment with endpoints (-3,2) and (7,2)?

Wit tester., two fathers and two sons went fishing . they caught only 3 fis...

two fathers and two sons went fishing . they caught only 3 fish and divided them equally among themselves without cutting. is it possible? how?

Example of negative number, Q. Example of negative number? If you take ...

Q. Example of negative number? If you take an elevator 8 stories  down , what would be the opposite of this? The opposite would be that you take the elevator 8 stories  up .

Imaginay Number, how to solve imaginary number such as like (-3v-5)² ?? Can...

how to solve imaginary number such as like (-3v-5)² ?? Can I cancel the radical sign and the power of two ? and square the -3 and times to -5 ? hope you will answer this :) thanks

Identify the surface for the equation , Identify the surface for each of th...

Identify the surface for each of the subsequent equations. (a) r = 5 (b) r 2 + z 2 = 100 (c) z = r Solution (a)  In two dimensions we are familiar with that this

Show that cos12+cos60+cos84=cos24+cos48 , L.H.S. =cos 12+cos 60+cos 84 =c...

L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12   R.H.S =c

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