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

GCF, Find the GCF of 70 and 112

Find the GCF of 70 and 112

Rounding, how do you round to the nearest dollars?

how do you round to the nearest dollars?

Elementary row operations, Anne, Betty and Carol went to their local produc...

Anne, Betty and Carol went to their local produce store to buy some fruit. Anne bought one pound of apples and two pounds of bananas and paid $2.11. Betty bought two pounds of appl

Factors, what are the factors af 34?

what are the factors af 34?

Determine the volume of the pool, An inground pool is pooring with water. T...

An inground pool is pooring with water. The shallow end is 3 ft deep and gradually slopes to the deepest end, which is 10 ft deep. The width of the pool is 30 ft and the length is

Polynomials, write the zeros of underroot3power2 -8x+4underroot 3

write the zeros of underroot3power2 -8x+4underroot 3

Matrices, how solve the inverse matrices using the matlab?

how solve the inverse matrices using the matlab?

Compute the probability of event, 1) Let the Sample Space S = {1, 2, 3, 4, ...

1) Let the Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8}. Suppose each outcome is equally likely. Compute the probability of event E = "an even number is selected". P(E) = 2) A s

Ellipsoid - three dimensional spaces, Ellipsoid Now here is the genera...

Ellipsoid Now here is the general equation of an ellipsoid. X 2 / a 2 + y 2 /b 2 + z 2 /c 2 = 1 Here is a diagram of a typical ellipsoid. If a = b = c afterw

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