1. Homework Statement
\frac{dy}{dx}\:+\:ycosx\:=\:5cosx
I get two solutions for y however only one of them is correct according to my online homework
(see attempt at solution)
2. Homework Equations
y(0) = 7 is initial condition
3. The Attempt at a Solution
\int \:\frac{1}{5-y}dy\:=\:\int...
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http://imgur.com/a/8QjoW
Hello-
I am trying to determine the dynamics of this linearly-damped hinge. Assuming that:
v(0) = 0
damping constant = b
door has mass = m
I was able to determine that:
∑Fx = -Fd * cos(45-θ/2) + Rx = m*dvx/dt
ΣFy = -Fd * sin(45-θ/2) - Fg +...
I am given the equations of Lorenz with respect to deterministic non-periodic flow:
\frac{dX}{dt} = Pr(Y-X), X(0)=X_{0}
\frac{dY}{dt} = -XZ + rX - Y, Y(0) = Y_{0}
\frac{dZ}{dt} = XY-bZ, Z(0) = Z_{0}
where Pr is the Prandtl number, r = Ra/Rac is the ratio of the Rayleigh number to its...
1. Homework Statement
Consider the following problems
In #2, they start the solution by saying: r(t)=u(t-1)
in #3, they start by saying that r(t)=t-tu(t-1)
I understand how to solve the problem once you get r(t), I just don't understand how they decide what r(t) is going to be.
1. Homework Statement
I need to solve:
x^2y''-4xy'+6y=x^3, x>0, y(1)=3, y'(1)=9
2. Homework Equations
3. The Attempt at a Solution
I know that the answer is: y=x^2+2x^3+x^3lnx
Where did I go wrong. I was wondering if it's even logical to solve it as an Euler Cauchy and then use variation...
1. Homework Statement
How exactly they combined equation1 and equation2 and got that system? I don't get that part.
2. Homework Equations
A*(dy/dt)= -k*y eq1
A*(dz/dt)=ky-kz eq2
3. The Attempt at a Solution
I tried substituting the 1st ky in the 2nd equation and then differentiating but...
1. Homework Statement
Express
\frac{d^{2}x}{dt^{2}} + \sin(x) = 0
In a system in terms of x' and y'.
2. Homework Equations
3. The Attempt at a Solution
I seen this example:
x^{\prime\prime\prime} = x^{\prime}(t)\cdot x(t) - 2t(x^{\prime\prime}(t))^{2}
Where they then wrote...
Hi,
I am learning ODE and I have some problems that confuse me.
In the textbook I am reading, it explains that if we have a separable ODE: ##x'=h(t)g(x(t))##
then ##x=k## is the only constant solution iff ##x## is a root of ##g##.
Moreover, it says "all other non-constant solutions are separated...
1. Homework Statement
So they want me to obtain the general solution for this ODE.
2. Homework Equations
I have managed to turn it into d^2y/dx^2=(y/x)^2.
3. The Attempt at a Solution
My question is, can I simply make d^2y/dx^2 into (dy/dx)^2, cancel the power of 2 from both sides of the...
1. Homework Statement
Solve for the solution of the differential equation and use the method of variation of parameters.
x`` - x = (e^t) + t
2. Homework Equations
W= (y2`y1)-(y2y1`)
v1 = integral of ( g(t) (y1) ) / W
v2 = integral of ( g(t) (y2) ) / W
3. The Attempt at a Solution
yc= c1...
Use laplace Transform to solve this ode:
So I got:
sV(s)-V(0)-12V(s)=U(s+5)
V(s)(s-12)=U(s+5)+1
V(s)=[U(s+5)+1]/(s-12)
Now to go back to time domain with Inverse Laplace Transform...My question is, how to transform U(s+5)/(s-12)?
Any help?
Thanks guys
I am trying to find the steady states in the ODE system. Assuming y0 = 2.5 * 10^5, I want to calculate y1, y2, y3 at the steady state. I do not understand how this would be possible, because only y0 is given and the following:
d0 = 0.003,
d1 = 0.008,
d2 = 0.05,
d3 = 1,
ry = 0.008,
ay = 1.6/100...
1. Homework Statement
Solve the following equation.
2. Homework Equations
( 3x2y4 + 2xy ) dx + ( 2x3y3 - x2 ) dy = 0
3. The Attempt at a Solution
M = ( 3xy4 + 2xy )
N = ( 2x3y3 - x2 )
∂M/∂y = 12x2y3 + 2x
∂N/∂x = 6x2y3 - 2x
Then this equation looks like that the integrating factor is...
Could someone tell me an application of the model of free fall to industry or more generally by using newton's second law and the law of gravitation, construct a model similar to the free fall one, that has an application in industry
1. Homework Statement
x²y''+xy'+(x²-0,25)y=0
y1= x^-1/2*sin x
2. Homework Equations
Abel's equation:
W= c.e^-(integrate (p(t))
3. The Attempt at a Solution
My Wronskian gave me a first order ODE that I really don't know solve.
x^-1/2*sinx y' + (1/2 x^-3/2 sin x- x^-1/2cosx) y2
I don't...
1. Homework Statement
I want to find conditions over A,B,C,D to observe a stable limit cycle in the following system:
\frac{dx}{dt} = x \; (A-B y) \hspace{1cm} \frac{dy}{dt} = -y \; (C-D x)
2. Homework Equations
Setting dx/dt=0 and dy/dt=0 you can find that (C/D , A/B) is a fixpoint.
3...
1. Homework Statement
Find the general solution f(t) of the differential equation: f''(t) − f'(t) − 12f(t) = 36π . How many free parameters enter the solution, and why?
2. Homework Equations
f = fH + fP where fH is the homogeneous solution and fP is the particular solution.
3. The Attempt at...
If i have
3y" - 2y' -y = 14 + e2x+8x
And i want to find the general solution.
Obviously first i obtain the characteristic eqn, yc, by making it into a homogeneous eqn. Then i can get yp
BUT
Am i able to get yp for the e2x and the 14 + 8x separately, then add them together for yp?
Thanks
1. Homework Statement
Given the differential equation
(\sin x)y'' + xy' + (x - \frac{1}{2})y = 0
a) Determine all the regular singular points of the equation
b) Determine the indicial equation corresponding to each regular point
c) Determine the form of the two linearly independent solutions...
Hello,
I'm recently trying to code a solver for a system of differential equations u'(t) = F(t,u), using a Runge Kutta 4 method with an adaptative stepsize. For this, I'm using the 'step doubling' method, which is the following : suppose that we now the solution u(i) at time t(i). Then, the...
1. Homework Statement
Y''-((Y')^2)+(C1*exp(Y))=C2
C1 and C2 are constants.
exp = e
2. Homework Equations
No clue how to start this
3. The Attempt at a Solution
Y'=A=dY/dt
Y=At+C3 (not sure)
A'-(A^2)+C1exp(At+C3)-C2=0
A'-(A^2)+C1exp(C3)exp(At)=0
let C=C1*exp(C3)
A'-(A^2)+Cexp(At)=0
dx/dt = x-y^2 dy/dt= x^2 -xy -2x
For each critical point, find the approximate linear OD system that is valid in a small neighborhood of it.
I found the critical points which are (0,0),(4,2),(4,-2) but have no idea how to do the above question! please help!
Hi there,
in my notes for Heun's method for solving an ODE, I have
y(new) = y(old) + 0.5(k1 + k2)Δh
And k1 is supposed to be f(y(old)) while k2 is f(y(old) + q11k1Δh) and q11 is 1
So if for example I have a simple differential equation like du/dt = au
It would be du/dt = 0.5(k1 + k2)
du/dt...
Im trying to implement the implicit Euler method in high-performance software for micromagnetic simulations, where I'm restricted to using the driving function of the ODE (Landau-Lifshitz equation) and the previous solution points. This obviously not a problem for an explicit method, since we...
1. Homework Statement
I've been stuck on this problem for three days now, and I have no clue how to solve it.
Construct a linear differential equation of order 2, for which { y_1(x) = sin(x), y_2(x) = xsin(x)} is a set of fundamental solutions on I = (0,\pi) .
2. Homework Equations...
1. Homework Statement
Suppose an RC series circuit has a variable resistor. If the resistance at time t is given by by R = a + bt, where a and b are known positive constants then the charge q(t) on the capacitor satisfies
(a+bt) q' + (1/C)q = V
where V is some constant. Also q(0) = q_0
Find...
I have a question regarding the solutions to linear-ordinary differential equations. I had originally learned that the solutions to such differential equations consist of a homogenous solution and particular solution. The homogenous response is due to initial conditions while the particular...
I need to find a trapping region for the next nonlinear ODE system
$u'=-u+v*u^2$
$v'=b-v*u^2$
for $b>0$.
What theory i need to use or wich code in Mathematica o Matlab could help me to find the optimal trapping region.
During the summer, I plan on learning differential equations (ODE's and PDE's) from bottom to top, but I am unable to choose books due to a great variety present. Can you suggest books for me to read in the following order (you can add as many books in each section if you like);
Ordinary...