Hi guys,
I am a Erasmus student in Vienna. Due to the difference between the plans in my home universtity and Vienna, I have to deal with having to take Parcial differential equations without having done Differential Equations 1 or 2.
In accordance with my university, I should take here...
Homework Statement
Find the general solution to the following differential equations
y'1 = -12y1 + 13y2 +10y3
y'2 = 4y1 - 3y2 - 4y3
y'3 = -21y1 +21y2 +19y3
The Attempt at a Solution
I'm a little unsure about what to do at the end, or what form to put it in.
The eigenvalues are
λ1 =...
Homework Statement
w= f(x,y)
x = u + v Verify that Wxx - Wyy = Wuv
y = u - v
Homework Equations
The Attempt at a Solution
I know how to find Wu or Wv but I have no idea on how to proceed to find the 2nd order derivative (or 3rd,4rth etc.. obviously). I...
Homework Statement
Here is the entire problem set, but (obviously) you don't have to do it all, if you could just give me a few hints on where to even start, because I am completely lost.
Recall that we found the solutions of the Schrodinger equations
(x^2 - \partial_x ^2) V_n(x) =...
Hi,
I have to modelize the buckling of a column and I've come up with this system:
N'(x) + N(x) \theta ' (x) \theta (x) - Q \theta ' (x) + f = 0
Q'(x) + N(x) \theta ' (x) + Q \theta ' (x) \theta (x) = 0
with f a constant
The coefficients (thetas) are not constants.
I've written it...
Hello all. I am having a very serious problem. The question states:
Find the value(s) of δ such that the solution of the initial-value problem
y'' − 4y = sin x;
where y(0) = δ and y'(0) = 0
is bounded.
I have no problem "solving"...
Hello team PF! I have been out of touch from calculus for quite a while and have been trying to solve a differential equation which I believe is nonlinear and non-homogenous. Haven't found any thread much relevant here, so I need this new one. The problem is as follows:
-(d2 u)/(dx2 ) + γ*u...
Can anyone help with these problems? I have no idea where to start. What is the general approach?
Determine the solution of ∂ρ/∂t = (sin x)ρ which satisfies ρ(x,0) = cos x.
Determine the solution of ∂ρ/∂t = ρ which satisfies ρ(x,t) = 1 + sin x along x =-2t.
Relevant equations: ∂ρ/∂t +...
Linearize and classify the fixed points of
\frac{d\theta1}{dt} = \Omega + sin \theta1 + \frac{1}{2} (sin\theta1 + sin\theta2)
\frac{d\theta2}{dt} = \Omega + sin \theta2 + \frac{1}{2} (sin\theta1 + sin\theta2)
I know that if the absolute value of omega is less than two, there will be 4...
Here's the problem i need help on. It can be found in Nagle's Differential Equations 8th edition chapter 8.3 number 32.
http://hostingbytes.us/images/3/6025942.jpg
i first tried to solve this using the power series and got:
a2=a0
a(k+2) = 2ak/(k+2)
after this, i have no idea how to...
A bar opens at 6 and is quickly filled with customer,the majority of whom are cigarette smokers.The bar has ventilators which exchange the smoke-air mixture with for fresh air.Cigarette smoke contains 4% carbon monoxide anda prolonged exposure to a concentration of more then 0.012% can be...
About serval differential equations where A, B, D, g, \chi, c are functions of r
\begin{eqnarray}
&-\frac{{\chi}'}{r}+\frac{c'}{c}\left(\frac{g'}{g} -{\chi}'\right)=\frac{e^{\chi}(q A B)^2}{r^2 g^2 c^2}& \\
&c c''+c c'\left(\frac{g'}{g}+\frac{2}{r} -\frac{{\chi}'}{2} \right)=-\frac{B'^2}{2...
1. A body of mass 2kg is initially at rest and is acted upon by a force of (v - 4) Newtons where v is the velocity in m/s. The body moves in a straight line as a result of the force.
2. a. Show that the acceleration of the body is given by dv/dt = (v - 4) / 2
b. Solve the differential...
I'm currently studying ODE's from Boyce's 'Elementary differential equations and Boundary value problems', It's a good book and it also explains some physical applications of differential equations, but I'm looking for a book that its main topic is about how to write differential equations for...
Hi,
Could some one help me to solve the equations ?
dX =sqrt(X) dB
where X is a process; B is a Brownian motion with B(0,w) =0;sqrt(X) is squart root of X.
Homework Statement
Solve the following differential equation for q(t) (position):
q''-qω^2 = C, where C is a time-independant value (basically a constant)The Attempt at a Solution
This equation is not homogeneous, therefore it must be non-homogeneous.
However, in every definition of...
I have following Differential Equations
a1*x2+b2*x1-c*cos(int(x3))*x4=d
-c*cos(int(x3))*x2-a2*sin(int(x3))+b2*x4=0
where a1,b2,c,d,a2,b2 are constants and x1=theta_dot; x2=theta_ddot; x3=alpha_dot; x4=alpha_ddot
I want to solve these equations for x1,x2,x3,x4 and want to plot with time.
When it is stated that a certain formula is solution to a differential equation, what does that mean in the physical world. What is the significance of a certain formula being a solution to a differential equation?
Hello experts!
Hope all of you will be fine.
I have an equation i.e. xy=c
And we all know it is hyperbola.
Now I say "graph some of the hyperbolas xy=c". Then kindly tell me how can we extract more than 1 graph from this single equation? And you will write the differential equations for...
Homework Statement
Solve the DE subject to y(1)=0. Forconvenience let k=v_r/v_s.
First let me apologize for the way it is written but I don't know how to use software like other on other posts I see.
Homework Equations
(dy/dx)= (v_s*y - v_r*sqrt(x^2+y^2)) / (v_s*x)
this may be...
Homework Statement
Not exactly a problem, more an example that has me confused :s
\frac{dN}{dt}=\kappa N-(\kappa/a^{2})N
This describes a population model where N is the population, \kappa is the net births (ie: births less deaths) and it doesn't tell you what a is (this in all the...
Hi,
I was reading a paper on control of the 1-D heat equation with boundary control, the equation being
\frac{\partial u(x,t)}{\partial x}= \frac{\partial^2 u(x,t)}{\partial x^2} with boundary conditions:
u(0,t)=0 and u_x(1,t)=w(t), where w(t) is the control input.
The authors...
Homework Statement
I've been having problems with a number of these things, here's the first one:
y'' -2y' -3y = -3te-t
Homework Equations
I know that the general solution will be
y = yh + yp
where yh is the general solution to the homogeneous equation, and yp
is the particular...
1. Homework Statement :
A function f : R → R is called “even across x∗ ” if f (x∗ − x) = f (x∗ + x) for every x and is called “odd across x∗ ” if f (x∗ − x) = −f (x∗ + x) for every x. Define f (x) for 0 ≤ x ≤ ℓ by setting f (x) = (x^2) . Extend f to all of R (i.e., define f (x) for all real x)...
If u(x,y) and v(x,y) are two integrating factors of a diff eqn M(x,y)dx + N(x,y)dy,
u/v is not a constant, then
u(x,y) = cv(x,y) is a solution to the differential eqn, for every constant c.
Homework Statement
One model for the spread of rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor.
i) Write a differential equation that is satisfied by y
ii) Solve the...
I'm given:
1. \frac{dX}{dt}=(X-1)(1-2X)
2. ln(\frac{2X-1}{X-1})=t
and asked to verify that it is an implicit solution to the first order DE given.
I successfully derived the second equation there to get:
\frac{dX}{dt}=\frac{-1}{(2X-1)(X-1)}
So now what? I tried several things and...
i have to solve the following differential equation :
dy/ dx + y = f(x) where f (x) = 2, 0 <= x < 1 and 0 if x >=1
and y (0)=0.
please explain how to solve it as it involves a discontinuous function ?
I am stuck while computing after computing the integrating factor e^x. Please suggest how...
Hi! I think I have to ask this since I'm having health problems-
from Kreyszig, for xy'=-y how do you verify the solution y=h(x)=clnx by differentiating
y'=h'(x)=-clnx^2? I don't see how you get the x^2 term
also for ODEs the solution is on an open interval a<x<b but how does it include...
Homework Statement
The deflection y of a non-uniform beam of length equal to 1, simply supported at both
ends and with uniformly distributed load q, is governed by the equation
(E*I(x)*y'')'' + k*y=q
y(0)=0, y''(0)=0, y(1)=0, y''(0)=0
I(x)=A[1-0.5(1-x)2]2, 0<=x<=1
where E =Young’s...
Homework Statement
Is the following equation a linear ODE?
\frac{d^{2}R}{dt^{2}}=-\frac{k}{R^{2}} where k is a constant
Homework Equations
A linear ordinary differential equation can be written in the following form:
a_{n}\left ( x \right )\frac{{d}^{n}y}{{d}x^{n}}+a_{n-1}\left ( x \right...
Homework Statement
Consider the system X'(t)=AX+B(t) where:
A =
[0 0 -1]
[1 0 -3]
[0 1 -3]
and B(t)=
[e-3t]
[et]
[3 ]
Find X(t) by frist determining P such that P-1AP=J is in Jordan form and then solving the three simple equations directly.
Homework Equations...
Homework Statement
Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions.
Homework Equations
The Attempt at a Solution
Homework Statement
1. Find he solution of the initial value problem:
x^2 (dy)/(dx) = 4y y(1)=2
2. Find the general solution of the differential equation:
(dy)/(dx) - 2y = e^(5x)
The Attempt at a Solution
i'm completely confused by this, no idea where to start. If...
Consider a string of length 5 which is fixed at its ends at x = 0 and x = 5. The speed of waves along the string is v = 2 and the displacement of points on a string is defined by the function f(x,t). At the initial time the string is pulled into the shape of a triangle, defined by
f(x,0) =...
I have to solve the differential equation (y')^2= 4y to verify the general solution curves and singular solution curves.
Determine the points (a,b) in the plane for which the initial value problem (y')^2= 4y, y(a)= b has
(a) no solution ,
(b) infinitely many solutions (that are defined for...
I have been given an equation : r^2 ( d^2R/dr^2) + 2r(dR/dr) - lambda*R = 0
It says to assume R~ r^β
Then i can't seem to spot how from that information we can produce this equation:
β(β − 1) rβ + 2β rβ − λ rβ = 0
Any help would be appreciated, thanks.
Homework Statement
(b) Find the differential equation for which –4xy3 + 4xy3sin(x) = –1 is an implicit solution on the interval (0, pi/2). Write your answer in the form dy/dx = f (x,y) where f (x, y) depends on both x and y.
The Attempt at a Solution
I'm not too sure on how to go about...
Homework Statement
Using power series, find solutions to the following DE
y' + y= x^2, y(1)= 2 and xo=1
Homework Equations
y(x)=an\sum(x-xo)^n for n=1 to infinity
The Attempt at a Solution
See the attachment
NOTE: I only want to find a way to collect all the x...
Homework Statement
Solve The following Equations:
2(y+3)dx-xydy=0
(x2-xy+y2)dx - xydy=0 use following assumption y=vx
xy3+ex2dy=0
The Attempt at a Solution
I am still a novice at diff eqs but here is what I got on the first one:
After seperating it I ended up with
(dx/x)=(ydy)/(2y+6) Then...
It’s a non-linear first order ode, the trig form of which is y’= sin(cx) sin(yx), y(0)=1. It’s possible that I’ve forgotten an important detail in the construction of the equation. If there’s someone who has some ideas about solving or approximating this, or who knows how to get mathematica or...
Homework Statement
find a particular solutions for the given differentiable equation.
Homework Equations
y''+5y'+6y=4-t^2
The Attempt at a Solution
Because the right-hand side is a polynomial of degree 1, so I want to have a particular solution of the same form. It's like...
At the moment, my first choice for a major is in Economics, and after doing some research, I've found out that the mathematics courses required for a PhD are Probability and Statistics, Single-Variable Calculus (Calc. 1 and 2), Multivariable Calculus, Linear Algebra and both Ordinary and Partial...
Homework Statement
If (x^2+1)dy/dx = xy for all y>0, and y(2) = 5, then y(3) = ?
Homework Equations
The Attempt at a Solution
dy/y = xdx/(x^2+1) -- use substitution with u=x^2
lny = 2(u+1)/du
lny = 2ln(x^2+1)+c
y = e^(2ln(x^2+1)+c)
5 = e^(2ln(5)+c)
5 = e^(ln25+c)
5 =...
Homework Statement
Find the exact solution of the initial value problem. Indicate the interval of existence.
Homework Equations
y'=e^(x+y), i.v.p:y(0)=0
The Attempt at a Solution
this is my attempt:
dy/dx=e^x+y=(e^x)(e^y)
--> dy/e^y=(e^x)dx
Integrating, -e^-y=e^x+C (C is...
Ok so here's my summarized story.
At the end of summer should be the start of my Senior year, but i dropped out and started college a year ago. I taught myself Calc I in two weeks while taking 18 credit hours and CLEPed out of it my first semester and received a 99.4% in Calc II the next...
1. LAW OF COOLING PROBLEM!HELP PLEASE! :)
At 1:00pm, Sally puts into a refrigerator a can of soda that has been sitting of temperature 70degF. The temperature in the refrigerator is 40degF. fifteen minutes later 1:15pm, the temperature of the soda has fallen to 60degF. At some time later, Sally...
Hi,
I've come across a problem in my differential equations book that I can't seem to be able to solve (it's not a homework problem, I'm just practicing):
"Using matrix algebra techniques and the method of undetermined coefficients, find a general solution for
x''(t) + y'(t) - x(t) +...
I was working on a simple differential problem which caused me some confusion
original eq =
dy/dx = -x/2y
which can easily be altered into
y dy = (-x/2) dx
This finally transforms into (after antiderivatives are determined)
(y^2/2) = -(x^2/4) + c
While I can see that this...