Not register? Register Now!
Essay Available:
You are here:
Pages:
17 pages/≈4675 words
Sources:
No Sources
Level:
APA
Subject:
Mathematics & Economics
Type:
Math Problem
Language:
English (U.S.)
Document:
MS Word
Date:
Total cost:
\$ 39.95
Topic:

# Differential Equations Mathematics & Economics Math Problem (Math Problem Sample)

Instructions:

Differential Equations: Using Undetermined coefficients

source..
Content:

1 u''+u'+2u= sin2t
The auxiliary equation is r2+r+2=0
Using the general formula
x=-b±b2-4ac2a
a = 1, b = 1, c = 2
x=-1±12-4(1)22(1)
x=-1±1-82
x=-1±1-82
x=-1±-72
x=-1+-72 or -1--72
∴If the roots are complex numbers, i.e r1= α+iβ , r2= α-iβ
Where α, β are real numbers, from the solution we have.
u(t)=eαt(c1cosβt + c2sinβt )
Hence -1±-72=α±iβ , where i= -1
-1±i72
-12±i72
Where α= -12 , β= 72
From the general solution,
2 ut=e-12tc1cos72t + c2sin7
3
4 2t u''+u=cosht where u0=1, u'0=4
The auxiliary equation is r2-1=0
r2=0+1
r2=1
Taking the square roots of both sides gives
r2=1
r= ±1
r1=1, r2=-1
From the general solution,
ut=c1er1t+ c2er2t
Substituting values of r1 =1 and r2= -1
ut=c1et+ c2e-t
Since gx= x2, we seek a particular solution (up)
Let the particular solution (up) = Ate2t+ Be-2t
Differentiating up,
up=Ate2t+ Be-2t

...
Get the Whole Paper!
Not exactly what you need?
Do you need a custom essay? Order right now:

### Other Topics:

• Pure Mathematics Economics Math Problem Research Paper
Description: If a regression model reveals the value of R squared = 0.69,then that times that the predictive model of the data set can account for 0.69=69% which is effective to make a judgment. The R-Square value expected range is between 0.60-0.90 which is translated to mean...
1 page/≈550 words| 2 Sources | APA | Mathematics & Economics | Math Problem |
• USING MATLAB TO ANALYZE THE DATA TABLES. Mathematics & Economics
Description: Read the questions in this document 2 Edit your responses into this document 1 Replace the text in blue italics with your responses 2 The associated data and/or original graphs are provided separately in an Excel spreadsheet where necessary....
4 pages/≈1100 words| No Sources | APA | Mathematics & Economics | Math Problem |
• Ecomomics Mathematics & Economics Math Problem Paper
Description: Marginal revenue is calculated by dividing the change in total revenue by the change in the quantity sold. This shows that the marginal revenue is the gradient (slope) of the total revenue curve. Marginal Revenue = Change in Total RevenueChange in Quantity Sold...
1 page/≈275 words| No Sources | APA | Mathematics & Economics | Math Problem |
Need a Custom Essay Written?
First time 15% Discount!