Initial value problem Definition and 172 Threads

Homework Statement The question is solve using laplace transforms: y" - 4y = 1-2t where y(0) =0 and y'(0) = 0 Ans is: y = t/2 - 1/4 + 1/4*e^(-2t) Homework Equations http://www.stanford.edu/~boyd/ee102/laplace-table.pdf" partial fractionsThe Attempt at a Solution (s^2)Y - sy(0) - y'(0) - 4Y =...

Homework Statement The equation 2y'' - y' + y^2(1-y) = 0 is a special case of an equation used as a model for nerve conduction, and describes the shape of a wave of electrical activity transmitted along a nerve fibre. Find a value of the constant a so that y = (1 + e^(ax))^(-1) is a...

Homework Statement Solve each of the following initial value problems: a) f'(x)=(x2-1)/x5 f(1/2)=3 Homework Equations The Attempt at a Solution I guess my problem with this is I'm not 100% sure what I'm being asked to do. I know I need to use integration to find the original...

Homework Statement Solve the following initial value problem y^{''} + 2y^{'} - 15y = 4\delta(t-2), \quad y(0) = 1, \quad y'(0) = -1. Homework Equations The Attempt at a Solution See figure attached for my attempt at the solution. Does anyone see any problems? Sorry if...

Hi all! I have quiet a lot a problems solving and programing with Mathematica this system of diff. equations: y'[x] == 1/b[x], b'[x] == 1/ubb 1/(y[x] + R1) 1/b[x] (uba 1/(y[x] + R1) - ub), b[0] == b00, y[0] == 0 y[2] == Sqrt[5] where ubb, uba, ub are functions: ub = b[x] -...

Homework Statement dy/dx=5y(1-y) y(0)=0.1 x belongs to [0; 2] Homework Equations The Attempt at a Solution dy/5y(1-y)=dx using partial fractions (1/(-y^2+y))=1/(y(1-y))= A/y+B/1-y multiplying both sides by (y(1-y)) gives 1=A(1-y)+B(y) when y=0 1=A so A=1 when y=1...

Homework Statement Solve the initial value problem Given: x=0, y=-2Homework Equations 2x(y+1)dx - ydy = 0The Attempt at a Solution Manipulating the given equation: --> 2x(y+1)dx - ydy = 0 --> 2xdx = ydy/(y+1) --> 2xdx = (1 - 1/y+1)dy --> 2x2/2 = y - ln(y+1) + lnC (where lnC is a constant)...

Homework Statement 1. To use Euler midpoint method to find an approx value to y(0.1) using a step size 0.1 2. To use integrating factor method to find exact value of y(0.1) 3. Determine the global error ( min 5 decimal places) Homework Equations f(x,y) = x+y, y(0) = 1.35 The...

Homework Statement Let f(t) be the solution to the initial value problem 2t(dy/dt)+y=t^4 with f(0) = 0 find f(t). Homework Equations The Attempt at a Solution I tried to do this by separating variables but that hasn't gotten me very far. I don't know if I can do it by doing...

Homework Statement Solve the initial value problem (y+e^-y)y'=sinx subject to y(pi)=0 Homework Equations The Attempt at a Solution I'm not quite sure what to do with this one. I've scanned through my book and could find no similar problems in what we've done so far. I tried to...

1) (dy/dx) = (1) / ( 2√x ) + 10 , y(1) = -1 2) (d^(2)r / dt^2) = ( 4 / t^3 ) ; (dr/dt) | t=1 = -5, r(1)=5 ... i have no idea where to start. what are the steps needed to figure out the answer...can someone please solve this for me! t thank you so much.

Solve the following given y(0) = 0 & y'(0)=1: y′′+3y′+2y = u2(t), such that u2(t) is a heaviside step function Here's what I've got so far, =>s2Y(s)−sy(0)−y′(0) + 3sY(s)−3y(0) + 2Y(s)= exp(−2s)/s Y(s) = (exp(−2s) + s) / (s(s2+3s+2)) Y(s) = exp(−2s)/(s(s2+3s+2))* + 1/(s2+3s+2)** The...

Homework Statement Solve the following initial value problem. Sketch the solution and describe its behavior as t increases. y'' + 4y' + 3y = 0 y(0) = 2 y'(0) = -1 1st i solved the characteristic: r^2 + 4r + 3 = 0 r = -1 r = -3 then the general solution is; y = c_1e^-x +...

Homework Statement dx/dt = 2*(1-x^2) with x(0)=0 Obtain the analytic solution to the IVP. Then, obtain the terms in the Taylor series up to and including the t^5 term. Note: should be possible to express x(t) in terms of hyperbolic functions. The Attempt at a Solution...

Homework Statement Use the Laplace transform to solve the following initial value problem: x' = 7 x + 5 y, y'= -2 x + e5t, x(0)=0, y(0)=0 Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s) Homework Equations...

General solution of initial value problem --dont understand problem is asking me?? Homework Statement Find a value for y-sub-0 for which the solution of the initial value problem: y' - y = 1+ 3sin t y(0) - y-sub-0 remains finite as t approaches infinity. (i called it "y-sub-0" , just...

Hi all! I'm having some trouble with the Existence and Uniqueness (E&U) thms. for ODEs. Consider the IVP: x'(t)=f(t,x(t)), x(\xi)=\eta In order to prove Existence, we need f to be Lipschitz or at least locally Lipschitz. For the Uniqueness we use the Banach's fixed point thm. for the...

Homework Statement How can I find a general solution to this problem: 5y" + 9y' - 9y = 0 Homework Equations The Attempt at a Solution I am confused with second order different equations in it

Homework Statement Suppose that the initial value problem y' = 7(x^2) + (5y^2) − 6, y(0)=−2 has a solution in an interval about x=0. Find y'(0) = Find y''(0) = Find y'''(0) = Homework Equations get it into standard form: dy/dt + p(t)y = g(t) find integrating factor =...

Homework Statement http://img40.imageshack.us/img40/7032/48975587.th.jpg http://img42.imageshack.us/img42/7264/solve2.jpg Homework Equations The Attempt at a Solution what I get is m^3e^(mx) + 10m^2e^(mx) + 9me^(mx) = 0 e^(mx) * (m^2 + 10m + 9) e^(mx) * (m+9)(m+1) m = -9 and m = -1 in...

Homework Statement Consider the initial value problem y'+e^(x)y=f(x), y(0)=1.Express the solution of the initial-value problem for x>0 as a non elementary integral when f(x)=1 and also in term of erf(x) Can somebody please help me solve this question? Thanks!

What is the general rule for determining how many initial conditions one needs to uniquely determine a solution of a set of ODEs or PDEs? is it simply the number of derivatives? How about for coupled differential equations? cheers M

Homework Statement Solve the initial value problem y" = 2x - y' , y'(0) = 1 , y(0) = 0 I know this is probably a simple problem but I don't have a book for the class yet and the teacher didn't really cover this material in class but we still have homework due on monday so i need to figure...

Homework Statement solve the IVP y''-8y'+16y=0 y(0)=2 y'(0)=7 Homework Equations The Attempt at a Solution auxiliary equation: r2-8r+16=0 (r-4)2=0 so we have r=4 with m=2 y(x)= c1e4x+c2xe4x y(0)--> c1e0 + 0 = 2 c1=2 now we have: y(x)=2e4x+c2xe4x take...

Homework Statement Find the first six nonvanishing terms in the Maclaurin series solution of the initial value problem (x^2 - 3)y''(x) + 2xy'(x) = 0 where y(0) = y0 and y'(0) = y1. Homework Equations The Attempt at a Solution Should with just something like Φ(x) such that Φ(x) =...

Homework Statement Solve the following IVP: \frac{dy}{dt} = \frac{1}{2y+3} y(0) = 1 Homework Equations The Attempt at a Solution \frac{dy}{dt} = \frac{1}{2y+3} \Rightarrow \int 2y + 3 dy= \int dt \Rightarrow y^2 + 3y= t +c where C is a constant Kinda stuck now. Any hints?

Homework Statement Find a second-order initial-value problem whose solution is sin at The Attempt at a Solution so i know that y' = a cos at y" = -a^2 sin at but the solution says that "Then y(t) = sin at is a solution to 2 y ''+ a y = 0 . Our initial conditions must be...

Laplace initial value problem... HELP! PLEASE! -------------------------------------------------------------------------------- Hello all! I'm stuck on this question: y''(t)+ 4y'(t) = sin2t y(0) = 0 solve it using laplace transform,... my final is tomorrow, and its 2 am, i...

Homework Statement Solve the given initial value problem and determine how the interval in which the solution exists depends on the initial value y0. y' = -4t/y, y(0) = y0 Homework Equations The Attempt at a Solution I solved the DE and got to: y = +/- sqrt(C - 4t^2)...

Solve: dy/dt = 4y-2, y(0)=3 I first separate variables: dy/(4y-2) = dt I then integrate both sides to get: ln|4y-2|=t + c I next set 4y-2=Ce^t Do I just plug 3 in for y to get C=10 or am I going about this problem the wrong way??

Homework Statement Solve the IVP dy/dt=4y-2, y(0)=3 This is how I work it. I integrate both sides and get y= 2y^2 - 2y + C I then solve for C: 3=2(0)^2 - 2(0) + C C = 3 Is this the correct way to solve for C?

Homework Statement solve: y" + 4y' + 4y = (3 + x)e-2x ... (1); y(0) = 2 & y'(0) = 5 Homework Equations using Undetermined Coefficients Method The Attempt at a Solution solving the associated homog. eq of (1) : y" + 4y' + 4y = 0 ... (2) we get: yc = c1 e-2x as m=-2 let...

Homework Statement I need to use the Laplace transformations to solve this IVP [SIZE="4"]y'-y=2cost(5t) , y(0)=0 Homework Equations The Attempt at a Solution I separated the question until the point Y(s)=(2s)/(s^2+25)(s+1) and then 2s=A(s+1)+B(s^2+25) I...

Homework Statement show the initial value problem x(dy/dx)=4y, y(0)=1 has no solution. does this contradict the existence theorem. please explain The Attempt at a Solution it is easy to find out a general solution is y=C*e^(4x), C is a constant. and for any x the right part of the...

Homework Statement Solve the initial value problem where y(0) = 2.Homework Equations dy/dt = 3 - 5(y^(1/2))The Attempt at a Solution I tried the separable equation method but when it came time to take the integral of 1/[3 - 5(y^(1/2)], every solution I got became too complex to solve for y...

Homework Statement Solve the initial value problem y'=y^2 , y(0)=1 and determine the interval in which the solution exists. The Attempt at a Solution So after solving the differential equation, we get y= 1/(1-t) However, I don't understand why the interval is only (- \infty , 1 )...

Repost with attachment >< 1. Homework Statement dy/dt + ty/(1+t^2) = t/(1+t^2)^1/2 y(1) = 2 Need to solve this initial value problem. The equation is a 1st order ODE 2. Homework Equations 3. The Attempt at a Solution I've attached my solution to the problem. Just...

Homework Statement dy/dt + ty/(1+t^2) = t/(1+t^2)^1/2 y(1) = 2 Need to solve this initial value problem. The equation is a 1st order ODE Homework Equations The Attempt at a Solution I've attached my solution to the problem. Just wondering if anyone can check my work. I...

I am trying to solve a differential equation using an integrating factor and the term I am trying to differentiate is (3*t+2*e^t)*e^(-3t/2) . I have tried simplifying it into these functions (terms, expressions): [(3*t)*e^(-3t/2)+2*(e^t)(e^(-3t/2)) =3t(e^(-3t/2))+2(e^(-t/2))...

Homework Statement Use the Laplace transform method to solve the differential equation y" -4y' +4y = e^2t subject to initial conditions y(0)=1, y'(0)=0 Homework Equations The Attempt at a Solution s^2Y(s) -sy(0) - y'(0) - 4[ sY(s) - y(0)] + 4Y(s)= L (e^2t) Y(s) [s^2 -4s...

Homework Statement y" + 2y' + 10y=0 y(0)=1 y'(0)= -1 solve initial value problem Homework Equations e^( ~ + iu)t= e^ ~t (cos ut + i sin ut) The Attempt at a Solution i've gotten pretty far into the problem, but i just can't seem to get the correct final answer. I changed y" +...

(t+1) dx/dt = x^2 + 1 (t > -1), x(0) = pi/4 I have attempted to work this by placing like terms on either side and then integrating. 1/(x^2 + 1) dx = 1/(t + 1) dt arctan x = ln |t + 1| + C x = tan (ln |t + 1|) + C pi/4 = tan(ln |0 + 1|) + C pi/4 = C x = tan (ln |t + 1|)...

When solving the initial value problem y ' = 2y-x, y(11)=6 using Eulers method with h=0.2, y0=? I know how to solve Euler's equations with the formula yn = yn-1 + F(xn-1 + yn-1)(h), however I'm not quite sure how or what they want in this particular case. Can anybody please help me out if...

Homework Statement Find solution for y'' + y' -2y = 2x with initial values of y(0) = 0, y'(0) = 1 Homework Equations I have found yc = c1*exp(-2x) + c2*exp(x), but finding yp is what I'm having trouble with... AND THEN I'm not so sure how to go about the initial value. The Attempt at...

Homework Statement I'm having problems with this IVP dy/dx=y^4-x^4 and y(0)=7 I know the answer is yes but I just don't see how to get it. Homework Equations The Attempt at a Solution

Laplace initial value problem... HELP! PLEASE! Hello all! I'm stuck on this question: y' + y = t sin t y(0) = 0 solve it using laplace transform,... my final is tomorrow, and its 2 am, i would appreciate a quick respone thanks in advance!

Solve the initial value problem y''+3y'+2y = 3e^{2t}+1 with initial values y(0) = 1, y'(0) = 1. I am unsure if I am going about the solution correctly. 1.) Find the characteristic equation. r^{2}+3r+2=0 \Rightarrow (r + 1)(r + 2) = 0 Therefore, y = c1•e^{-t}+c2•e^{-2t} 2.) Use method of...

Homework Statement A tank contains 3000 liters polluted water. The concentration of pollution is 5%. 50 liters per minute of the polluted water is removed and replaced with 50 liters of unpolluted water per minute. How much time will it take for the concentration to go down to 1%? 2...

Homework Statement Solve the initial value problem given x(2)=0 \frac{dx}{dt}=tx^{2}+2x^{2}t^{2} Homework Equations The Attempt at a Solution I factored out the x^2 and separated variables and integrated as follows: \int\frac{dx}{x^{2}} = \int t+2t^{2} dt...

Im having a little issue figuring out this intial value problem. Solve the Initial Value Problem y' = (3x^2)/[(3y^2)-4] where y(0)=1 Looks like I can solve it as a seperable DE. dy/dx = (3x^2)/[(3y^2)-4] [(3y^2)-4] dy = (3x^2) dx Integrating both sides... (y^3) - 4y =...