Concept explainers
Program Description: Purpose of problem is to find a particular solution of the system
Explanation of Solution
Given
The system of differential equation is
Explanation:
Consider matrix form of the system of differential equation as,
Consider
The non homogeneous term is a constant
Therefore, A constant particular solution is in the form as,
Substitute
Equate the coefficient to obtain first equation.
The second equation is obtained as,
Substitute
The value of
The particular solution of the system of differential equation is,
Substitute
Conclusion:
Thus, the particular solution of the differential system
Want to see more full solutions like this?
Chapter 5 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
- Solve the following equations. Be sure to check the potential solution(s) in the original equation, to see whether it (they) are in the domain. (a) log, (r? –x – 2) = 2arrow_forwardProblem 3 In class, we solved for the vorticity distribution for a "real" line vortex diffusing in a viscous fluid. Integrate this vorticity distribution to find the tangential velocity as a function of radius. Plot the velocity distributions for a a line vortex of circulation 0.5 mls in 20 °C air for times of 1, 10, and 100 seconds.arrow_forwardA 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5 pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5 gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows. Q' (t) = = (b) Find the quantity of salt in the tank as it's about to overflow. esc C ✓ % 1 1 a 2 W S # 3 e d $ 4 f 5 rt 99 6 y & 7 h O u * 00 8 O 1 9 1 Oarrow_forward
- Problem 1: Derive the general solution form for the recurrence t n =12t n-2 -16t n-3 +2^ n Show your work (all steps: the associated homogeneous equation, the characteristic polynomial and its roots, the general solution of the homogeneous equation, computing a particular solution, the general solution of the non-homogeneous equation.)arrow_forwardProblem 1 The position x as a function of time of a particle that moves along a straight line is given by: r(1) = (-3 + 41)c 0. f1 0.1t The velocity v(t) of the particle is determined by the derivative of r(t) with respect to t, and the accelerationa(t) is determined by the derivative ofv(t) with respect to t. Derive the expressions for the velocity and acceleration of the particle, and make plots of the position, velocity, and acceleration as functions of time for0arrow_forwardMechanics Arz Yahya, PH.D. Example 2: The 30-kg pipe is supported at A by a system of five cords. Determine the force in each cord for equilibrium.arrow_forwardarrow_back_iosarrow_forward_ios
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole