Concept explainers
In Exercises 3—6, a system, an initial condition, a step size, and an integer n are given. The direction field for the system is also provided.
(a) Use EulersMethodForSystems to calculate the approximate solution given by Euler’s method for the given system with the given initial condition and step size for n steps.
(b) Plot your approximate solution on the direction field. Make sure that your approximate solution is consistent with the direction field.
(c) Using HPGSystemSolver, obtain a more detailed sketch of the phase portrait for the system.
5.
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Differential Equations
- Construct a model for the number of cats, y, after x months that make use of the following assumptions: 1. It begins with two cats – one female and one male, both unneutered. 2. Each litter is composed of 4 kittens – 3 males and 1 female. 3. It takes four months before a new generation of cats is born. 4. No cat dies (all are healthy) and no new cats are introduced.arrow_forwardEvaluate the derived system of Linear equations from a given nodal analysis circuit using Gauss-Seidel Method. Tabulate the results and use a terminating condition of Ea <0.00001 for each variable. 0 = 5 I1 – 9 I3 + 3 I2 -8 = 2 I3 – 5 I2 + 3 I1 16 = 5 I2 + 10 I1 – 3 I3arrow_forwardIn Exercises 13–17, determine conditions on the bi ’s, if any, in order to guarantee that the linear system is consistent. 13. x1 +3x2 =b1 −2x1 + x2 =b2 15. x1 −2x2 +5x3 =b1 4x1 −5x2 +8x3 =b2 −3x1 +3x2 −3x3 =b3 14. 6x1 −4x2 =b1 3x1 −2x2 =b2 16. x1 −2x2 − x3 =b1 −4x1 +5x2 +2x3 =b2 −4x1 +7x2 +4x3 =b3 17. x1 − x2 +3x3 +2x4 =b1 −2x1 + x2 + 5x3 + x4 = b2 −3x1 +2x2 +2x3 − x4 =b3 4x1 −3x2 + x3 +3x4 =b4arrow_forward
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