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

Problem word solving, Mrs. Jones and Mr. Graham had the same amount of mone...

Mrs. Jones and Mr. Graham had the same amount of money at first. After Mrs. Jones bought a computer that cost $2,055, she had 1/4 as much money as Mr. Graham. How much money di

Kfso, poijn jjjnjb jbjdbjbj

poijn jjjnjb jbjdbjbj

Probability, Mike sells on the average 15 newspapers per week (Monday – Fri...

Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers

Finds out the center and radius of circle, Finds out the center & radius of...

Finds out the center & radius of each of the following circles & sketch the graph of the circle. a) x 2 + y 2 = 1 b) x 2 + ( y - 3) 2  = 4 Solution In all of these

Area of polygons, ho we can find the area of diffrent types of polygon

ho we can find the area of diffrent types of polygon

Trigonometry, what are reason inside a circle?

what are reason inside a circle?

Determine the team having similar code-pigeon hole principle, Shirts number...

Shirts numbered consecutively from 1 to 20 are worn by 20 members of a bowling league. While any three of these members are selected to be a team, the league aims to use the sum of

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