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- Quèstion 4 Determine the form of a particular solution y, for y" +y3Dcosxarrow_forwardA Moving to another question will save this response. Question 12 Find the solution of x²y" + xy-4y=0 where y(1) = 0 and y (1) = 4arrow_forwardKk.425. Sketch the time dependent solutions based on the on-dimensional phase line of:arrow_forward
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- Question 4: Linearize i + 2i + 2x? - 12x + 10 = 0. Around its equilibrium positionarrow_forwardProblem. 9: Let z = x? 7 xy + 6 y? and suppose that (x, y) changes from (2, 1) to (1.95, 1.05 ). (Round your answers to four decimal places.) (a) Compute Az. (b) Compute dz. ?arrow_forwardProblem 6. Find all constant solutions of the autonomous ODE y = (y? – 1) (y? – 4) and determine whether these solutions are respectively attractors, repellers, or neither.arrow_forward
- 1. A space-ship is heading towards a planet, following the trajectory, r(t) = (Ae-¹² cos(3t), √2Ae-t² sin(3t), - Ae-t² cos(3t)), where A 50, 000km and the time is given in hours. (a) The planet is centred at the origin and has a radius, rp = 2,000km. At what time does the ship reach the planet? Give your answer (in hours) both as an exact expression and as a decimal correct to 4 significant figures. (b) To 4 significant figures and including units, what are the velocity and speed of the space-ship when it reaches the planet?arrow_forward1. Solve for the orthogonal trgsctories y² = 4x*(1- kx) %3Darrow_forwardIn a 24-hour period, the water depth in a harbour changes from a minimum of 3/2 m at 2 am to a maximum of 7 at 8:00 am. Which of the following equations best describes the relationship between the depth of the water and time in the 24-hour time period? ³ (π (t− 2)) + ¹/7 d=-c COS (t− 2)) + ¹/7 d = −sin (π (t− 2)) + d= cos (π (t-2 1/ π d = sin (π (t− 2)) + 24/7arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,