What is Ivp: Definition and 144 Discussions

Let $A_{n\times n}$ be a matrix with real and distincts eigenvalues. Let $u(t,x_0)$ be a solution for the initial value problem $\overset{\cdot }{\mathop{x}}\,=Ax$ with $x(0)=x_0,$ then show that for each fixed $t\in\mathbb R,$ we have $$\lim_{y_0\to x_0}u(t,y_0)=u(t,x_0).$$

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Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement Instructions: You will need to use software for these problems. The goal is to find a number x0 such that the solution to the initial value problem x'=ƒ(t,x) x(0)=x0 passes through the given "target". Attach figures that you used to answer the problems. 1. Consider the...

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Homework Statement Use Laplace transforms to solve the initial value problems. ##y''+4y=0;## ##y(0)=5;## ##y'(0)=0## Homework Equations The Attempt at a Solution $$y''+4y=0$$ $$L(y'')+L(4y)=L(0)\implies s^{2}Y(s)-sy(0)-y'(0)+4(sY(s)-y(0))=0\implies s^{2}Y(s)+4sY(s)-5s-20=0$$...

Homework Statement y''+6y=f(t), y(0)=0, y'(0)=-2 f(t)= t for 0≤t<1 and 0 for t≥1 Homework Equations The Attempt at a Solution L{y''}+6L{y}=L{t}-L{tμ(t-1)} where μ(t-1) is Unit Step Y(s)=L{y} sY(s)-y(0)=L{y'} and y(0)=0 s2Y(s)-sy(0)-y'(0)+6Y(s) where y(0)=0 and...

Homework Statement Let y(x)=\sumckxk (k=0 to ∞) be a power series solution of (x2-1)y''+x3y'+y=2x, y(0)=1, y'(0)=0 Note that x=0 is an ordinary point. Homework Equations y(x)=\sumckxk (k=0 to ∞) y'(x)=\sum(kckxk-1) (k=1 to ∞) y''(x)=\sum(k(k-1))ckxk-2 (k=2 to ∞) The Attempt at a Solution...

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Find an interval centered about x=0 for which the given initial value problem has a unique solution. (x-2)y''+3y=x where y(0)=0 and y'(0)=1 I've seen the answer on a few different sites (1)(2) and still don't get it :mad: The question speaks of a unique solution with regards to an interval...

The given family of functions is the general solution of the D.E. on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y=c_1x+c_2x\ln{x} on (0, \infty) and x^2y''-xy'+y=0 and y(1)=3, y'(1)=-1 So plugging in y(1)=3 gives 3=c_1+c_2\ln{1} and...

Find the value of a ∈ R for which the initial value problem: (S) {(xy' +y)/(1+x2y2)=1 {y(0)= a has a solution and, for this value of a, find explicitly the maximal solution of (S). I'm assuming I first find the implicit solution of the original diff eq (which I'm not too sure how to do...

I need to find the explicit maximal solution of an IVP using exact Diff Eqs: The IVP is given as: {xexyy'-cos(x)+yexy=0 {y(0)=1 So I know at first I need to get the implicit solution by getting that: A(x,y) = xexy B(x,y) = -cos(x)+yexy I know I need to find the partial derivative of A(x,y)...

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Here is my question: Solve the initial value problem \(y\prime=\dfrac{3x^2}{3y^2-4},~y(1)=0\) and determine the interval in which the solution if valid. Hint: To find the interval of definition, look for points where the integral curve has a vertical tangent. My work so far...

Proof on Linear 1st Order IVP solution being "bounded" A function h(t) is called "bounded" for t≥t0 if there is a constant M>0 such that |h(t)|≤M for all t≥0 The constant M is called a bound for h(t). Consider the IVP x'=-x+q(t), x(0)=x0 where the nonhomogeneous term q(t) is bounded...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Here is the question: I have posted a link there to this topic so the OP can see my work.

Hi guys, I'm having trouble with a homework problem: I will have to solve for the IVP of a transport equation on R: the equations are: Ut-4Ux=t^2 for t>0, XER u=cosx for t=0, XER I've actually never seen a transportation problem like this and any help would be...

Hello, I am having trouble solving the below IVP, particularly I am confused with the w: du/dt = v - w(t-5) dv/dt = 2 - u(t) u(0)=0, v(0)=0 Any help would be great. Thank you.

Here is the question: I have posted a link there to this topic so the OP can see my work.

Here is the question: I have posted a link there to this topic so the OP can see my work.

Here is the question: Here is a link to the question: Can someone help me solve this: y'+tan I have posted a link there to this topic so the OP can find my response.

Re: Logan's question at Yahoo! Answers involving an IVP with a linear 1st order ODE How would I solve a DE like t(dy/dt) + 7y = t^3 dy/dt +7y/t = t^2 Then do I need to find the integrating factor?

Here is the question: Here is a link to the question: Initial value problem? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: Consider the initial value problem for y; Laplace? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement I've got an IVP where, 3xy+y2+(x2+xy)y'=0, y(1)=0 The Attempt at a Solution I've solved to get, x2y(x+\frac{1}{2}y)=0 Is it correct to say, x=0 or y=0 or y=-2x, Since y= 0 is the only solution that fits y(1)=0, then y=0 \forallx

Homework Statement Find a nontrivial solution of the IVP dy/dx = tx^p (p is any number); y(0) = 0 Does this violate the uniqueness part of the Existence/Uniqueness Theorem? ExplainHomework Equations The Attempt at a Solution I've found two solutions: one for p = 1 and one for all other...

Homework Statement \frac{d^2y}{dt^2} + t\frac{dy}{dt} + t^3y = e^t;\ \ \ y(0) = 0, \ \ y'(0) = 0 Show that the solution is unique and has derivatives of all orders. Determine the fourth derivative of the solution at t = 0.2. The attempt at a solution I'm somewhat lost here... Trying to...

Homework Statement f(x,y) = y' = \frac{y+x^2-2}{x+1} , y(0) = 2 Write the formula for the 2nd order Taylor approximation I just want to ask a question Homework Equations Taylor seriesThe Attempt at a Solution Taylor: y(x) = y(x_0) + y'(x_0)(x-x_0) + \frac{y''(x_0)(x-x_0)^2 }{2} = \\...

Here is my problem, I have been trying this for a couple of hours. I have sought help with a professor, and yet we still couldn't get it. Here is the question in full. Consider the initial value problem below to answer the following. a)Find the approximations to y(0.2) and y(0.4) using Euler's...

Homework Statement Here is the question with the solution from the textbook: I don't get how looking at (2/t) and 4t tells us that the solution must be on the interval 0 to infinity. Don't we have to set y' to zero and solve for how the directional fields behave and thus find out how y...

Homework Statement Consider the interaction of two species of animals in a habitat. We are told that the change of the populations and can be modeled by the equations \frac{dx}{dt}= 0.1x-0.8y \frac{dy}{dt}=-0.2x+0.7y Find the solution to the above equations with initial values x(0)=9 and...

Homework Statement Sketch the solution to the IVP u_{t}+uu_{x}=0 \\ u(x,0) = e^{-x^{2}} Homework Equations Monge's equations \frac{dt}{d\tau} = 1 \\ \frac{dx}{d\tau}=u \\ \frac{du}{d\tau}=0 The Attempt at a Solution I think I do not really need the Monge's equation, but I have no...

Homework Statement Suppose that f has the intermediate value property on an interval J, that g has the intermediate value property on an interval I and that g(I) is a subset of J. Prove that f°g has intermediate value property on I. Homework Equations The Attempt at a Solution I...

Homework Statement Suppose f has the intermediate value property on an interval I and let k be a constant. Prove that kf has the intermediate value property. Homework Equations The Attempt at a Solution Since f has IVP on I, then there is distinct a and b in I and f(c)=v exists...

Solving an IVP using Laplace Transforms. HELP! Ok I'm supposed to Solve this problem using Laplace Transforms. \frac{d^2 x}{dt^2}+2\frac{dx}{dt}+x = 5e^{-2t} + t Initial Conditions x (0) = 2 ; \frac{dx}{dt} (0) = -3 so I transformed the the IVP and it looks like this s^2 x(s) - s...

Homework Statement Use Laplace Transform to Solve IVP y"-2y'+2y=e^(-t) y(0)=0 y'(0)=1 Homework Equations [s^2*L{y}-sy(0)-y'(0)]-[2sL{y}-y(0)]+2L{y}=0 (for Homogeneous eq)The Attempt at a Solution Homogeneous Attempt: L{y}=1/(s^2-2s+2) Not sure if correct There soluton to this point is...

Not sure of solution for IVP Homework Statement (x^2)*y"+4*x*y'+4*y=0 y(1)=1 y'(1)=2 Homework Equations Start with r(r-1)+4r+4=0 then (r^2)+3r+4=0 get (-3+/-7i)/2 The Attempt at a Solution Leads to y=C(1)e^(-3t/2)cos(7t/2)+C(2)e^(-3t/2)sin(7t/2) More y'=... one large...

Homework Statement Let f : (-1, 1) → ℝ. f satisfies the intermediate value property and is one-to-one on (-1, 1). Prove f is continuous on (-1, 1) The Attempt at a Solution I was thinking that the IVP and one-to-one implies that f should be strictly monotonic and that a strictly monotonic...

Homework Statement y'' + 4y = sin(2t) y(0) = 1 y'(0) = 1 Homework Equations cramers ruleThe Attempt at a Solution after isolating Y(s) i end up with: Y(s) = 2 / (s^2+4)^2 + s/(s^2+4) after i do partial fraction decomposition, i get 4 equations with 4 unknowns, A, B, C and D i inserted B...

Homework Statement given: (y-xy)y' = y^(2) + 1 y(0)=0 Homework Equations So I subbed y^(2) = u The Attempt at a Solution w/ u=y^(2) i got... (y-xy)y' = y^(2) + 1 (1-x)yy' = y^(2) (1-x)(u'/2) = u + 1 and it is here that I am stuck! I [think] I have to put...

Homework Statement Given the equation mx''+cx=cAsin(Ωt) with the initial conditions x(0)=0 and x'(0)=0. Solve the initial value problem for the case when Ω < ω and show that |x(t)| < H provided A < H(1-(Ω/ω)). Homework Equations The Attempt at a Solution For my solution to...

Homework Statement y''+6'+10y=0 y(0)=2 y'(0)=1 Homework Equations The Attempt at a Solution Laplace everything and I get s^2*Y(s)-2s-1+6s*Y(s)-12+10Y(s)=0 isolate Y(s) Y(s)=(2s+13)/(s^2+6s+10) split into 2 terms, bottom can be rearranged by completing the square...

Homework Statement Solve the initial value problem y' = 2cos (2x)/(3+2y), y(0) = 1 and determine where the solution attains its maximum value Homework Equations The Attempt at a Solution I got it to here y^{2} + 3y = sin(2x) + C but I don't know what to do from here... Help please

IVP Laplace Transform Problem -- Tricky Inverse Laplace Transform Homework Statement Solve x"+x'+x=1, given x(0)=x'(0)=0 Homework Equations The Attempt at a Solution Plugged in transforms: s2*Y(s)-s*y(0)-y'(0)+s*Y(s)-y(0)+Y(s)=1/s Plugged in initial value points, simplified...

I'm working on a problem for my diffEQ's class. It reads: For each of the given initial value problems, what is the region where the existence and uniqueness of the solution is guaranteed? Is it all t, or t > -3, or a neighborhood of t = 1? a) x'' = t x x' + sin(t) b) x'' = tx + 2x' +...

Hello everybody, I was wondering whether someone has more information on the influence of inconsistant initial conditions on solving a system of ODE's with periodic solutions using a time marching method like a 4th order Runge-Kutta scheme. The phenomenon I am studying is described by a...

Homework Statement Find a particular solution to this IVP: dy/dx = 1 - 2y y(0) = 5/2 2. The attempt at a solution I find -0.5 *ln (1- 2y) = x + C However, y = 5/2 gives ln(-4), which is a problem...Have I done something wrong? Any suggestions please? How to find a family of...

I am trying to solve an IVP problem and I seem to be stuck on it because I am getting an integration that seems very complicated and I think I messed up on it, I have my work so far below. Homework Statement Find the solution to the IVP ty^'+7y=2t^2 e^2t, y(1)=7 Is this equation...