In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.
Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.
Hi, sorry if this is posted/answered all the time, but I need some book advice.
Basically, I will be taking this course in the fall:
And required prep knowledge for entering this course is:
Now I've taken tons of Linear Algebra and Multivariable calculus, but I need brush up on...
Hello everyone!
My professor was going over a problem real fast for the exam and now that i went over it again, I'm lost on how he did this last step. He is using a method called Abels Theorum. THe problem says:
Find a second solution of the given differential equation:
t^2y''+3ty' + y = 0...
I'm confused on how to equate coniffecents. What I'm doing is, finding a particular solution for just the polynomial then I'm going to find it just for the exponential and add them together rather then putting it all together and making it a mess, but I'm stuck when i try to add the...
Look whos back! I ran into another problem, i redid the problem twice and i keep coming out with the same answer!
here is what i have:
http://img139.imageshack.us/img139/6205/lastscan5qw.jpg
This is waht I submitted which was wrong...
Can't figure out this seperable diffEQ! :(
Hello everyone 'ive been trying to figure out this easy looking Differential Equation and yet its wrong! weee!
Here is the problem:
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/58/6217226076d5fd259f53ad1e3ed4071.png
has an implicit...
I'm having trouble with this problem. Actually I'm having trouble with all of this set of problems (when the eigenvectors are complex). I must not be finding these things correctly, because nothing is matching up with the book. Any help would be awesome.
\vec {x}\,' = \left( \begin{array}{cc}...
I'm working on this project that involves air drag. The model for the air drag is given as:
\vec F_d = \frac{1}{2} C \rho A v^2
I'm using Newton's Second law in relation to this force and gravity (in one dimension) which yields:
a = \frac{1}{m} \left( -mg + \frac{1}{2} C \rho A v^2...
Ok, we just started this chapter, and I am slightly confused with one specific aspect of the info... I'll just go through an example, it's the best way to explain it IMHO.
I have to find the Laplace transform of the following function.
The table of transforms that I can use are (sorry about...
YATP - Yet Another Trainlike Problem
Sailboats A and B each have mass 60kg and cross the starting line at the same time of a race. Each has an initial velocity of 2m/s.
Obviously from this, m1 = m2 == 60kg and vo1 = v02 == 2 m/s.
The wind applies a constant force of 650N to each boat and...
Sup' all?
Ok, I have a quick question (hopefully). I'm trying to use the method of undetermined coefficients, and I keep getting stuck at one specific spot in the method. I'm not exactly sure what I'm doing. Let me try and explain:
The problem is given as:
2y''+3y'+y=t^2+3*\sin t
Which...
Ok, I have this modeling problem that I cannot figure out how to setup.
The problem is given:
The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 200,000...
This problem is from section 5.2 in Boyce, DiPrima's Differential Equations 8th edition.
(1 - x)\,y''\,+\,y\,=\,0
I get:
2\,a_2\,+\,a_0\,+\,\sum_{n\,=\,1}^{\infty}\,\left[(n\,+\,2)\,(n\,+\,1)\,a_{n\,+\,2}\,-\,n\,(n\,+\,1)\,a_{n\,+\,1}\,+\,a_n\right]\,x_n\,=\,0
Which leads to one...
I am suppose to find the power series solutions to some diffeqs.
y'=xy
The method is to assume that
y=\sum_{n=0}^{\infty}{c_nx^n}
is a solution to the diffeq.Then since we can differenitate term by term we have
\frac{d}{dx} \left[ \sum_{n=0}^{\infty}{c_nx^n}...
Hello everyone, well thus far in our introduction to Laplace Transforms I am understanding much of what is being shown, however I am having the unsatisfying task of having to solve the following DiffEQ,
y^3-8y=\sum_{k=0}^{3}\delta(2t-k\pi), y(0)=0, y'(0), y"(0)=0
I am having a great...
A water tank has the shape obtained by revolving the parabola x^2=by around the y-axis. The water depth is 4ft at noon when a circular plug at the bottom of the tank is removed. At 1pm the depth of the water is 1ft.
a)find the depth y(t) of water remaining after t hours
b)when will the...
I am having a lot of trouble solving this problem. I don't even know where to start. Any help would be greatly appreciated.
A 30 year old woman accepts an engineering position with a starting salary of $30000 per year. Her salary S(t) increases exponentially with S(t)=30e^(t/20) thousand...