Tagged Questions

31 views

solving system of equations(nonlinear)

I am trying to solve the following system of equations: $$\frac{kq^2}{d}=mg(L-L\cos(t))+\frac{kq^2}{r}$$ $$\sin(t)=\frac{x}{L}$$ $$r^2=(L-L\cos(t))^2+(x+d)^2$$ The parameters are: $k,L,d,q,m,g$ The ...
56 views

solving the system

solve the system : $$y+|x-2|=3$$, $$|x+y|= m$$ graphicly when $m$ equals $6$. I can easily (realtively) skecth the first graph , however, how the bloody hell do you sketch $|x+y|= 6$??
23 views

45 views

Solving system of 3 equations

How do I solve the following system? $$\left\{ \begin{array}{} x_o = 4 - x_r \\ x_r = -2 - x_s \\ x_s = 2 - x_r \end{array} \right.$$ All the techniques i've found for solving 3-equation ...
32 views

Find the height of the dam given angles of a triangle

The top of a dam has an angle of elevation of 1.3 radians from a point on a river. Measuring the angle of elevation to the top of the dam from a point 155 feet farther downriver is 0.8 radians; assume ...
70 views

Math Constraint Problems

This is a homework problem of mine. The professor said we can use any resource to help us solve and I cannot get up with anyone from class. Please help. I'm not looking for a direct answer, I ...
50 views

14 views

Time-Scale Decomposition: The slow variable only has a single unstable steady state?

I'm completing a time-scale decomposition of a set of equations. The original set of two equations is $$S'= 3k_1S^3E_T + (3k_{-1}-3k_1S^3)E_1$$ $$E_1'=-k_1S^3E_T+(k_{-1}+k_2+k_1S^3)E_1$$ I was ...
39 views

Given a solution flow to find periodic solutions

Given the system of differential equations $x' = 2x + y^3$ and $y' = -y$ i found the flow $$\phi_t(x,y) = ((x_0 + 1/5y_0^3)e^{2t} - 1/5 y_0^3e^{-3t}, y_0 e^{-t})$$. I am wondering are there any ...
28 views

Compute the solution $\phi_t \overrightarrow x_0 = e^{At} \overrightarrow x_0$ to the system $x' = -x + 4y$ and $y' = -4x - y$

Compute the solution $\phi_t \overrightarrow x_0 = e^{At} \overrightarrow x_0$ to the system $x' = -x + 4y$ and $y' = -4x - y$ The characteristic equation i found is $\lambda^2 + 2\lambda + 17$...The ...
57 views

Coupled mass spring system with damping and initial values

After researching through the web, I can't figure out how to express into a differential equation a coupled mass spring system with damping and initial values. Two masses and two springs, no external ...
90 views

92 views

Problem: Determine the equation of the circle that passes through three points, $J(-3, 2)$, $K(4, 1)$, and $L(6, 5)$. I thought of using systems like so: $$\left\{ \begin{array}{rcl} (x+3)^2 + ... 4answers 110 views How to solve the following system of equations. 2x^2-3xy+2y^2=2\frac{3}{4}\\x^2-4xy+y^2+\frac{1}{2}=0 I tried all the methods that I know, but I could't isolate x or y to form one equation. 0answers 30 views Let r_t+ru_x+ur_x=0 and u_t+uu_x=0 for u(x,0)=f(x) and r(x,0)=g(x). Let r_t+ru_x+ur_x=0 and u_t+uu_x=0 for u(x,0)=f(x) and r(x,0)=g(x). I know I have to solve for implicit u first and then r, but I don't know if I'm using the right method here. What I've ... 1answer 46 views Consider the system x'= \frac{-x}{2}; y' = 2y + x^2  to solve the system and find topologically conjugacy and show topologically conjugate Consider the system x'= \frac{-x}{2}; y' = 2y + x^2  Show that this system is topologically conjugate to the linear system \overrightarrow {y'} = DF_{(0,0)} \overrightarrow {y} a) Solve both ... 1answer 79 views Find solution for the following system: x'=y^3-4x , y'=y^3-y-3x Find solution for the following system: x'=y^3-4x , y'=y^3-y-3x As I found the three equilibrium points, (0,0) , (-2,-2) , (2,2) . I am wondering how to find the solution for this one ... 1answer 50 views find all the equilibrium points for x'=y^3-4x , y'=y^3-y-3x Consider the system x'=y^3-4x y'=y^3-y-3x What is the systemic way to find all the equilibrium points for this system? My approach is to set both x' and y' to 0 , solve the two equations ... 1answer 50 views Simplifying a coupled-pendulum equation by assumption I have been given the following question and I am unsure if I am missing an assumption or if I am misunderstanding something else: Two identitical pendula each of length \ell and with bobs of ... 0answers 45 views How to solve a system of equations with 3 variables?$$13 = V_{pf} \cdot (0.0518)+V_{bf} \cdot \cos\theta_b0=-V_{pf} \cdot (0.9659)+5V_{bf} \cdot \sin\theta_b845=V_{pf}^2+5V_{bf}^2 Okay, so I'm at the very last part of a word problem and ...
I have the plane autonomous system $\dfrac{dx}{dt}=x(1-2x-y)$ $\dfrac{dy}{dt}=y(1-x-2y)$ I need to show that the axes of the phase plane and the line $x=y$ are solution trajectories, but I don't ...