1. M

    second order differential equation with two variables, please have a look

    Dear Sir, Madam, I hope you are doing well.. At first let me introduce myself.. I am Mudhar an international Ph.D student in the University of Bradford, United Kingdom working in modeling of reverse osmosis units for wastewater treatment. Actually I have stacked with a solution of second order...
  2. E

    A finite group with exactly two conjugacy classes has order 2.

    Is this proof valid? Let Z=Z(G). Because of the class equation, either |Z| = 1 or |Z| = 2. If |Z| = 2 we are done. Suppose |Z|=1. Then there exist a g not belonging to Z and the class equation is |G| = 1 + |G| / |N(g)|, from which |G| / (|G| - 1) = |N(g)|. As |N(g)| is an integer, the only...
  3. A

    order of integration, triple integral

    Hi I am struggling to get going on the following problem: V is the region bounded by surfaces x=0 and x=9-y^2 -9z^2 express the integral int int int f(x,y,z)dV as an iterated integral in two orders: (i) dx dy dz and (ii) dy dx dz I am having trouble trying to figure out the region V so I can...
  4. K

    Second order differential equation

    Hello everyone I am struggling a bit with a couple of math challenges and hope some of you can help or give a hint. First of all the following differential equation is given: a_{0} \cdot y'' + a_{1} \cdot y' +a_{2} \cdot y = 0 I am then to show that if \lambda_{0} is a double root to the...
  5. Jason76

    Finding a DE from a 2nd Order General Solution

    In order to find a DE from the general solution of a first order equation, we use implicit differention, so should we try implicit differentition twice to find the DE from solution to a 2nd order equation? How about y = c_{1}e^{-2x} + c_{2}e^{3x} ? Now if we had a general solution to a first...
  6. sakonpure6

    Homogenous Fourth Order ODE

    Hello! I have the homogenous ODE y^{(4)}+4y=0 and I seek the general solution. My approach: \lambda^4 = -4 \implies \lambda = \pm2i \, \text{of multiplicity 2} . So the general solution is: y(x)=c_1cos(2x)+c_2sin(2x)+c_3xcos(2x)+c_4xsin(2x) However the solution manual says the general...
  7. M

    Order of Operations Calculator

    From speaking with teachers and students, I use Standard PEDMAS. I'm open to updates for this calculator. Order of Operations Calculator
  8. O

    Trigonometrically fitted runge kutta for solving second order ivps

    Please who can put me through this topic or have tangible material on this....thanks
  9. R

    Solution of first order wave equation

    Hello The d'Alembert solution of the following wave equation u_{tt}=c^{2}U_{xx}, 0<x<1 u(x,0)=f(x), u_{t}(x,0)=g(x), u(0,t)=u(1,t)=0 is given by u(x,t)=\frac{1}{2}(f(x+ct)+f(x-ct))+\frac{1}{2c}\int_{x-ct}^{x+ct}g(x)dx My question, what is the d'Alembert solution if -1<x<1, and...
  10. S

    help on first order ode smoking in a room

    can anyone help me on question a) and b) when i solved the ODE given i got 3e^(1/30000)t + c for b) not the one given in the answer
  11. S

    help on this first order ODE

    for this question i get dx/dt = 1/10000 - x/50000 where does 30000 come from
  12. S

    finding resonance 2nd order ODE

    for question b) the answer says 5 but how do you find it can you explain it to me?
  13. S

    2nd order ODE deriving equations

    im learning to apply 2nd order ODE on spring mass system letting y(t) the displacement from equilibrium position i have my''(t) = mg - T - R R = beta*y'(t) T = ks s is the stretch length then i have my''(t) = mg - k(s+y) - beta*y'(t) m''(t) = -ky - beta*y'(t) my''(t) + beta*y'(t) +...
  14. R

    rotation of segment in different order

    hi , there are given are two rotations: R1 and R2, and a line segment AB. the image of R1R2(AB) is a line segment that is parallel to the line segment R2R1(AB). my kindly request is to the reason they are parallel. i know that in both cases AB is rotated by the same angle but that is not...
  15. M

    Integration resulting from the solution of a 2nd order ode

    Hi , I got this integration when i tried to solve a 2nd order ode, any hints about solving it? $$\int_0^s (c_1+c_2 z)(c_3+c_4 z)^{c_5} \cdot e^{(c_6+c_7 z)}z \, dz$$ Thanks MH
  16. D

    Order of operations

    Good evening all, real basic question if I may? I have the following problem in front of me and apparently I have the correct answer of -7.74 put I do not understand where the (3.3)^2 comes into play in regard to the question or order of operations... here goes: 2.5-(3.1+0.5/5)^2 (3.3)^2...
  17. E

    Forming first order differential equations(MODELLING QUESTION)

    Hi, I am slightly confused as how to form a differential equation for this problem. I have an idea for equations, but based on the correct answer I can't see where I'm going wrong. Nuclear reactor in meltdown. Rate of internal heat generation= mckt , m is mass of reactor, c is average specific...
  18. M

    Vertical line from a point in order to creating new vector

    Hi, I am trying to make a graph on desmos software I want someone to insert degrees of three lines (with sliders) B1,B2,B3 (for instance 0 , 350 , 320) Then I want the vertical line from a point (slider) in first line B1 which intersects B2,B3. (New points created S1,S2,S3) Finally I measure...
  19. S

    Finding solution to 2nd order using Laplace Transforms

    Hi, I have this problem that states: Solve the following initial value problem: y'' - 25y = 50t, y(0) = 0, y'(0)=0 I get stuck at the end and I'm really confused about how to finish solving it so I was hoping someone on here could help me. Here's what I've done so far: Denote \mathcal{L}[y]...
  20. J

    Need help with Procedure and Order of Ops

    I'm trying to figure out what I'm doing wrong in these problems. Here is what I did for both of them: Imgur Imgur I'm using the method of cross multiplying to get the numerator and multiplying across to get the denominator. It worked for a/b + b/a and 1 / 1 + (1/x-1) and 4a/b + b/4a but...