### General Solution : ODE's

Find the general solution of the ODE below: y" + 2y' + 101y = 0

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Find the general solution of the ODE below: y" + 2y' + 101y = 0

Problem A: Suppose that a giant HD-ready television of mass m falls from rest towards earth and its parachute opens at time t=0. when its speed is v(0)=v0 Since the TV is massive assume the drag force is proportional to the square of the velocity. Write a complete model for the velocity v(t) What is the asymptotic behavi

Solve the linear Differential Equation (see attachment) y'-y=exp(2x) y(0)=0 y"+6y'+10y=0 2yy'=1-y^2 y(0)=-2.

A steel ball weighing 128 pounds (mass= 4 slugs) is suspended from a spring. This stretches the spring 128/485 feet. The ball is started in motion from the equilibrium position with a downward velocity of 9 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet p

Solve {see attachment} for y(x) using the change of variables z = y + x.

Use methods of undetermined coefficients to find one solution of: y'' + 2y' +2y = (10t+7)e^(-t)cos(t)+(11t+25)e^(-t)sin(t)

Find y as a function of x if: (x^2)(y'') + 19xy' +81y = x^2 y(1) = 9 y'(1) = -3 Hint: First assume that at least one solution to the corresponding homogeneous equation is of the form . You may have to use some other method to find the second solution to make a fundamental set of solutions. Then use one of the two metho

Find particular solution to differential equation 3y'' + 4y' + 1y = 1t^2 -2t + 2e^(-3t)

Use the method of undetermined coefficients to find one solution of : y'' - 16y' +101y = 16exp(8t)cos(6t)+16exp(8t)sin(6t)+1*1

Find solution of: y'' - 2y' + y = 16exp((5)t) y(0)=1 y'(0)=6

Find y as a function of x if (x^2)(y'')-7xy'-9y = x^2 y(1)=6 y'(1)=8

Find all solutions to the ODE yy'= (1-y^2) sin x. (When dividing by 1-y^2, be careful that you don't lose any solutions). NOTE: y2 = y squared Please see attached file for full problem description.

Find y as a function of t if 64y'' + 32y' +4y = 0 y(5)=6 y'(5) = 5

Find y as a function of t if 16y'' - 88y' +121y = 0 y(0) = 4 y'(0) = 9

Find y as a function of x if: (x^2)(y'') - 5xy' -16y = 0 y(1)=2 y'(1)= 9

Please see the attached file for full problem description. --- Here is the problem: Find the center of mass of the region bounded by the parabola y = 8 -2x^2 and the x-axis a) if the density lambda is constant and b) if the density lambda = 3y

In order to solve differential equations, it is helpful to classify them as belonging to one or more categories. In this entry we will consider three common classes of first order ordinary differential equations (ODEs): separable, exact and linear. We will show how each class is defined.

This question is part of a study guide for my final test. Solve the following initial value problem. (see attached for problem) Thank you

(d^2 * y)/(d * t^2) + 6 * (dy/dt) + 9y = 0 y(0) = 10, y'(0) = 0

Solve a Function (see attached) Explain why the Euler's method cannot be used to approximate y(2)

Consider the Sturm-Liouville problem (pu') + Vu = 0 for the function u(x), with p(x) > 0 and V(x) = q(x) + lambda p(x). (a) Perform the Prufer substitution u - r sin theta and u'p = r cos theta and obtain the Prufer equations for the amplitude r(x) and the phase theta (x): r' - 1/2 ((1/p) - v) r sin 2 theta, theta' = (1/p)

State if the equation is separable or homogeneous: (x^2 + y^2) (dy/dx) = 5xy

Solve the initial value problem; it is not necessary to find all solutions of the equation: xy'=y(y-2), y(3)=2.

Solve the initial value problem dy/dx=(3x^2+4x+2)/[2(y-1)], y(0)=-1

Find the solution of the system X' using the "diagonalization" technique (actually the Jordan form in this case) Please see the attached file.

I would like someone to introduce me to ODE and answer questions as they arise.

Suppose that a rabbit is initially at point (0,100) and a fox is at (0,0). Suppose that the rabbit runs to the right at speed Vr = 5 ft/sec and the fox always runs toward the rabbit at speed Vf = 6 ft/sec. Write a Matlab program that determines to within 1 second, when the fox catches the rabbit. The program should also plot rab

Sketch the direction fields for the following ODE's. Make use of isoclines wherever possible. a. y' = y - x + 1 b. y' = 2x c. y' = y - 1 d. y' = xsquared + ysquared - 1 e. y' = y - xsquared Please note y'=y prime. It looks diff, when i see the ? #2. In each direction field above sketch integral curves for which

Y'= 1/2 - (X)+2x when y(0)=1 Find the exact solution of ___ O/ <<note!!!! I don't know how to put in a zero with a line going across to make a pheee. 1a. Let h=.1 use euler & improved to approximate to get "Phee" of .1, phee of.2, and phee of .3