1. B

    Show that Bessel function satisfies ODE

    Show that the function, , satisfies the equation . Attempt at the solution, Therefore, by substituting into ODE of interest, But, Substituting back into ODE, At this point I am stuck. I tried playing around with the bottom limit of the summation on the LHS of the...
  2. B

    Show a derivative satisfies an equation

    Would someone mind checking this for me? Show that $y=x|x|$ satisfies the equation $\frac{dy}{dx}=2\sqrt{|y|}$ If $x>0$, then $y=x^2$ Hence $\frac{dy}{dx}=2x=2\sqrt{|x^2|}=2x$ If $x<0$, then $y=-x^2$ Hence $\frac{dy}{dx}=-2x$ as $x<0$, $-2<0$ we have a negative times a negative which is...
  3. J

    Finding the solution to differential equations that satisfies the initial condition.

    dP/dt=8sqrt{pt}, P(1)=6 This is my working and i prove that it does satisfy the initial condition but apparently i am still incorrect: dP/sqrt{p}=8sqrt{t}dt Integrating both sides we get: 2sqrt{p}= (16t^3/2)/3 + C Using P(1)=6: 2sqrt{6}= (16(1)^3/2)/3 + C C= 2sqrt{6} -16/3 Substituting...
  4. A

    Find a nonhyperbolic matrix which satisfies certain conditions

    For $e^{At} = 1/2\begin{bmatrix}e^{2t}+e^{-t} & e^{2t} - e^{-t} \\ e^{2t}-e^{-t} & e^{2t}+e^{-t}\end{bmatrix}$ for all t $\in$ $\mathbb{R}$. how to find A?
  5. A

    Find a nonhyperbolic matrix which satisfies certain conditions

    A nonhyperbolic matrix A for which the planar system $\overrightarrow x' = A \overrightarrow x$ has an equilibrium point at (0,0) with the x-axis as a stable curve and the y-axis as an unstable curve. Does this matrix exist? if so, could you show me that matrix?
  6. R

    look for the value that satisfies the equation

    please explain how can I answer this one :) I know the answer should be a.) -4 & b.) -1. could you explain how will I come up with that answer? Thank you :)
  7. W

    Is there a composite number that satisfies these conditions?

    we know that if $q=4k+3$ ($q$ is a prime), then $(a+bI)^q=a^q+b^q(I)^{4k+3} =a -bI(mod q)$ for every gaussian integer $(a+bi)$ ,Now consider a composite $N=4k+3$ satisfies this condistion for $a+bi=3+2i$, I use Mathematica8 and find no solutison$ less than $5\cdots 10^7$, can someone find a...
  8. S

    Find an equation for the hyperbola that satisfies the given conditions. Urgent help

    Vertices (0, ±16), hyperbola passes through (−5, 24)
  9. R

    Finding if this recursively defined sequence satisfies this explicit formula

    Hey Guys. Having a bit of trouble with recursion and seeing if the sequence satisfies the formula. I need to determine whether ak=2ak-1+k-1 for all integers k>=2 satisfies the explicit formula an=(n-1)2 for all integers n>=1 Not quite sure on what the right steps are. Thanks for your...
  10. D

    Trying to find a sequence that satisfies specific characteristics

    [SOLVED]Trying to find a sequence that satisfies specific characteristics Hi everyone! I heard this is a great place to get/give help with math questions/explanations. I was wondering if someone could help me out. I'm trying to find a sequence xn that satisfies ' Ʃ|xn|2 < infinity ' and...
  11. M

    What is an example of a model that satisfies ZFC?

    From what I know, a model is a set of things that "give" an "interpretation" of the axioms such that the axioms are true of the "things" in the set. Is this right? I know there are many, many examples of such "sets of things," models, interpretations, structures, etc. of ZFC, but I don't have...
  12. B

    find the particular antiderivative that satisfies the given condition

    C'(x)=2x^2-5x ; C(0)=3000 C(x)=
  13. slevvio

    Showing that the dual space of bilinear maps V x W -> R satisfies tensor property

    Let U,V and W be finite dimensional vector spaces, and define B to be the vector space of all bilinear maps V \times W \to \mathbb{R}. Given a bilinear map \alpha : V \times W \rightarrow U, define \tilde{\alpha}: B^* \rightarrow U^{**} by \alpha(\psi)(\sigma) = \psi (\sigma \circ \alpha)...
  14. T

    How to show that a function satisfies a differential equation?

    Hi I'm doing a biology based maths course and this is driving me crazy, I just don't quite know how to show that this function satisfies the differential equation? Obviously I'm not expecting you guys to do this for me, but if you could just point me in the right direction, I don't know if I...
  15. S

    Find a polynomial of degree 3 with real coefficients that satisfies...

    Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.?Zeros of -3,-1, 4, and P(2) = 5 I am attempting this problem in order to study for an upcoming test. I am stuck on this one, and would really like to learn if someone could please assist me, I would very...
  16. L

    Confirm that the given function satisfies a differential equation.

    Question in the attactment ! Please help me guys ! :(
  17. M

    Show that y(x) satisfies equation

    Assume that the implicit function e^{xy} = y determines y as a differentiable function of x in some interval. Without attempting to solve the equation for y(x), show that y(x) satisfies the differential equation (1-xy)y' - y^2 = 0. I started by finding the derivative of y. y' = y'e^x...
  18. H

    Show a solution satisfies the DE

    hey . i need the solution : 1- y‘= 1+y^2 . y= tan (x+c) 2- y‘‘+2y‘+10y=0 . y= a cos pi x + b sin pi x 3- y‘‘‘= cos x . y= - sin x + ax^2 + bx + c
  19. J

    Showing that iteration f(x)=x(2-Rx) satisfies 1-Rx_{n+1}=(1-Rx_n)^2, etc

    Hi, I have the following exercise... I have solved the first question, but I don't know about the second question. Thanks for whatever help you have give me! Since early electronic computers had no automatic division, it was necessary to accomplish this by a process of calculating reciprocals...
  20. M

    Showing that a function satisfies an ODE

    Hi, I have the following problem and I am stuck... Thanks for any help you can give me! The problem says: The atmospheric pressure p>0 decreases with height x according to the equation dp/dx=-gk where k is the air density, and g is the (constant) acceleration due to gravity. The...