Simplify equation into a 2nd order DE and convert it into system of 1st order DE's

Simplify equation into a 2nd order DE and convert it into system of 1st order DE's -r/R 8 e 1 d rk dr for RsrsR+ w,...
Match the following with the correct answer.
1 1st order reaction of all reactant = A 1/k 2 1st order reaction of one reactant = B ln(2)/ 3 2nd order reaction of one reactant = c kin R-K[A] - d[Al/dt 4 rate constant = D A +B- C 5 rate = E Rin R-k[A] - d[A]/dt 6 half time of 1st order reaction = FAAC 7 lifetime of 1st order reaction = GAB
5. (15 points) Consider 3 dz r dr d, 20. a. Convert the integral to rectangular coordinates with the order d: dr dy (but don't evaluate.) b. Convert the integral to spherical coordinates (but don't evaluate.)
5. (15 points) Consider 3 dz r dr d, 20. a. Convert the integral to rectangular coordinates with the order d: dr dy (but don't evaluate.) b. Convert the integral to spherical coordinates (but don't evaluate.)
1. Classify each ordinary differential equation as to order (1st, 2nd, etc) and type (linear/nonlinear). a) y' + 2y + 3y = 0 b) y" + 2yy + 3y = 0 c) y" + 2y' + 3xy - 4e" y sin 3
cos(()dr - (r sin(O) - e)de = 0, r(0) = 1 (make r the subject of the formula)
2. (8 points) Solve the linear, 1st order ODE with initial value: dy dr 3. (7 points) Find all critical points and the phase portrait of the autonomous Ist order ODE dy dr -5y+4 Classify each critical point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves in the regions in the ry plane separated by equilibrium solutions. dy dx (S points) Solve the Bernoulli equation:-(- 31-1 7. (8 points) Solve the ODE by variation of parameters: -4y+4y (+...
(4) Consider the 2nd order equation for a mass-spring-damper system, mx'' + bx' + kx = f(t) a) Assuming f(t) is a step function, find the Laplacian transform, X(s) (include terms for the initial conditions xo, vo). b) Assume m = 1, b = 5, and k = 6, and x(0) = 3, x’(0) = 0. Find the time-domain solution (take the inverse transform). (5)Find the Laplace transform of y(t) from the differential equation, assuming u(t) is a step function....
Ch 15 Extra credit opportunity. 10 pts max. Due By Exam 2 (11/14). 1)If you are enrolled in or have previously taken calculus, derive the integrated rate equations for oth, 1st and 2nd order reactions. (2 pt ea, 6 pts) Hint, start with the instantaneous rate law, expressed as differential rates, Such as d[A]/dt = k. Separate your variables, d[A] to one side, dt to the other. Integrate from time 0 to time t and simplify. Show every step. 2)...
Solve the given 2nd Order DE (t-1)y'' - ty' + y = (t-1)e^2t, y1 = t
2. Given the nonhomogeneous 2nd order differential equation y" +2y = xe*: (8 pts) a. Identify the forcing function (ie. the nonhomogeneous term we call f(x)). b. Write the homogeneous equation associated with this DE. c. Find the particular solution to the homogeneous DE from part b which satisfies the initial conditions y(0) = 2, y'(O)=-1. (note: you will NOT be using technique of undetermined coefficients)
Given the equation, d-3.(C ( +8-e)-F c) . Simplify and implement the equation in ladder diagram. Give appropriate details of NO and NC contact.
Given the equation, d-3.(C ( +8-e)-F c) . Simplify and implement the equation in ladder diagram. Give appropriate details of NO and NC contact.