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

Adding fractions with different denominators, Q. How to Add Fractions with ...

Q. How to Add Fractions with Different Denominators? Ans. Here's the main thing to remember about adding fractions with different denominators-you can't! Fractions with di

Toni tiger, Application Practice Answer the following questions. Use Equat...

Application Practice Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Sav

Trignometry, i have to get 10 points in 10th class

i have to get 10 points in 10th class

Determine the approximate raw act score, Using the same mean and standard d...

Using the same mean and standard deviation as mean m = 20.1 and a standard deviation s = 5.8. Joe was informed that he scored at the 68 th percentile on the ACT, what was Joe's ap

Determine the function f ( x ) , Determine the function f ( x ) .       ...

Determine the function f ( x ) .             f ′ ( x )= 4x 3 - 9 + 2 sin x + 7e x , f (0) = 15 Solution The first step is to integrate to fine out the most general pos

Probability, A man enter a lucky draw that requires him to pick five differ...

A man enter a lucky draw that requires him to pick five different integers from 1 through 30 inclusive .he chooses his five number in such a way that the sum of their log base 10 i

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

Projectile, what is the greatest projection range down an inclined plane? h...

what is the greatest projection range down an inclined plane? how we will calculate that?

Practice, #question.Mai is 3 years ypunger than twice the age of her brothe...

#question.Mai is 3 years ypunger than twice the age of her brother .If b represents .

Midpoint rule - approximating definite integrals, Midpoint Rule - Approxima...

Midpoint Rule - Approximating Definite Integrals This is the rule which should be somewhat well-known to you. We will divide the interval [a,b] into n subintervals of equal wid

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