The existence and uniqueness theorem for ordinary differential equations (ODE) says that the solution of a 1st order ODE with given initial value exists and is unique. It is discussed briefly on p. 528 of the text.<<< this just talks about the ability for a differential eqn. to have practical importance in predicting future valu
Solve the Initial Value Problem y'' + 4y' + 5y = 35e^(-4x) given: y(0) = -3, y' (0) = 1
LaPlace Transform : Solve y'' + y = Sqrt2Sin(t Sqrt2), with y(0) = 10 and y' (0) = 0 using the method of the LaPlace Transform.
Solve y'' + y = Sqrt2Sin(t Sqrt2), with y(0) = 10 and y' (0) = 0 using the method of the LaPlace Transform.
Fundamental set of solutions of a Differential Equation : Verify that e^x Cos(2x) and e^x Sin(2x) form a fundamental set of solutions of the differential equation [ y'' - 2y + 5y = 0 ] on the ...
Verify that e^x Cos(2x) and e^x Sin(2x) form a fundamental set of solutions of the differential equation [ y'' - 2y + 5y = 0 ] on the interval (- infinity, infinity). With the e^x the "x" is the only upper score in the problem. The Cos and Sin are on the regular line of the problem.
General Solution of the Higher-Order Differential Equation : 16 d^(4) y / dx^(4) + 24 d^(2) y / dx^(2) + 9y = 0
Could you provide assistance on setting up and working of the problem. 16 d^(4) y / dx^(4) + 24 d^(2) y / dx^(2) + 9y = 0
Fundamental Set of Differential Equations on an Indicated Interval : y'' - y' - 12y = 0; e^-3x, e^4x, (-∞, ∞ )
Y'' - y' - 12y = 0; e^-3x, e^4x, (-∞, ∞ ) Could you provide assistance on setting up and working of the problem.
I could use your assistance with a problem. The problem is to be soulved by using MATLAB. I have the stu version 6.0. I'm not real familure with using it, if you could show me the code on the problem I would greatly appriciate it. I have tried for a long time with no headway. I'm sorry, I wrote the problem in complete. t
ODE - Lagrange's Equation : y=x(1+y')+(y')^2
Bernoulli Differential Equation : y''-(3/(2y))*((y')^2)-2*y =0
Find the function "f(x)" which this sum converges to on the I.O.C.. ∞ Σ ((n+1)x^n)/(2^n) n= 0
Hi, these three problems are from Calculus II. (See attached file for full problem description)
(See attached file for full problem description) --- Find the volume of the solid generated when the region R bounded by the given curves is revolved about the indicated axis. Do this by performing the following steps A sketch the region R B show a typical slice properly labeled C write a formula for the approximate vo
What fraction of the area of a square is closer to the center of the square than to any edge of the square? This one is harder than it looks! I am looking for an exact answer, but you can get a rough numerical estimate by a Monte Carlo method , and this might help you check your answer. I have no idea where to begin this prob
(See attached file for full problem description with proper symbols and equations) --- First: solve these problems. Second: check my answers. Third: if my answers are wrong explain why. Let . Explain whether or not the Mean Value Theorem applies on the interval [1,8]. If it does, find the number c that is guarant
I need only the answers with short explanation to the attached questions. I just need to check my answers and correct myself where i have gone wrong.
If its possible to answer these three questions using mathematica 5 if matlab looks similar, or the commands are similar then i guess matlab is fine... if its at all possible for mathetmatica it would be much appreciated Using Newtons Method 1. Plot f(x) = a on the interval - 3 ≤ x ≤ 3. a) Use Newton
Our problem is to determine which values of D result in extinction and which result in survival. This can be done by studying equation (*), treating D as a bifurcation parameter see Section 2.6 a. Using technology to study solutions to an equation (*) for parameter values of 08, 0.7, 0,4, and 0.5. For each choice of D, use se
The function is f(x) = 5x^2 / (x^2 + 2) I need to find the x and y intercepts all asymptotes and inflection points. I know only how to do this if I have a closed interval if you could walk me through this step by step use the critical number and f'(x) and f''(x) graph
(See attached file for full problem description with equations) --- Let . (a) Find the set of points at which . (b) Let . Find a set V such that f takes U onto V in a one-to- one fashion and the inverse function g on V. ---
File is attached. I need only the answers with work shown in very shortly. I just need to check my answers.
Differential Equation (IX): Formation of Differential Equations by Elimination Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.
Find the general solution of each of the differential equation y ''- y ' = x2 . If the solution is not valid over the entire real axis, describe an interval over which it is valid. If k is a nonzero constant, prove that the equation y ''+ k2y = R(x) has a particular solution 1 y given by ..... Find the general solution of
Prove that the spheres x2 + y2 + z2 = 16 and x2+ (y+5)2 + z2 =9 intersect orthogonally.
The presence of toxins in a certain medium destroys a strain of bacteria at a rate jointly proportional to the number of bacteria present and to the amount of toxin. If there were no toxins present, the bacteria would grow at a rate proportional to the amount present. Let x denote the number of living bacteria present at time t.
For what position of the point (x, y) is the sum of the distance from (x, y) to the x-axis and twice the distance from (x, y) to the point (0, 1) a minimum?
For what position of the point (x, y) is the sum of the distance from (x, y) to the x-axis and twice the distance from (x, y) to the point (0, 1) a minimum? From Advanced Calculus, Taylor & Mann(1972), p.144
Please explain how to evaluate the limit lim/k arrow to 0 f(x = h) - f(x)/h using the rules for finding the derivative of f.
11. Consider an electric circuit like that in Example 5 of Section 8.6. Assume the electromotive force is an alternating current generator which produces a voltage V(t) = E sinwt , where E and w are positive constants (w is the Greek letter omega). EXAMPLE 5. Electric Circuits. Figure 8.2(a), page 318, shows an electric circu
Vectors, Force and Work (12 Problems); Cross Product, Orthogonal Vectors and Area of Parallelogram (7 Problems); Parametric and Symmetric Equations (12 Problems)
Please see the attached files for the fully formatted problems.
Rate of Change : Using the equation d(t)=3tsq.rt.2 - 5 determine the rate of change between 8 seconds and 12 seconds.
Using the equation d(t)=3tsq.rt.2 - 5 determine the rate of change between 8 seconds and 12 seconds.