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20 Nov 2019
solve all of them please
Answer for (c): P(t) = 3 + 67e-at 4. Find the solution to the following initial value problem 8y3 cos(7t)0, y(0) 2 Answer: y(t) 5. Find the solution to the following IVP ty -2y - 3t3 cos(4t), y(T/80 Answer: y(t)tsin(4t) 6. Consider the differential equation dy = y(y2-4)(y2 + 9) dt (a) Find the equilibrium solutions of the ODE (b) Construct a phase diagram and determine the stability of the critical points (c) Make rough sketches of typical solution curve:s Answer to a portion of (b): cr.pts. -2-unst. 0-st.2-unst 7. Find the solution to the following IVIP - tan Answer: y(t)-5t tan(t)-5 cos(t 8. Find an explicit expression for the solution y of the following initial value problem 2- y(1) = 2, t-1. 9. A glass of cold soda is placed into a room held at 30 C. (a) If k is a (positive cooling constant), find the differential equation satisfied by the temperature, T (t) of the soda (b) Find the soda temperature as a function of time (and k), if the initial temperature of the soda was 2 C. (c) If after 40 minutes the soda temperature was 10 C, find the cooling constant k nswer: (a) T(T-30): (b) T() 30 - 28e: (e)n(
solve all of them please
Answer for (c): P(t) = 3 + 67e-at 4. Find the solution to the following initial value problem 8y3 cos(7t)0, y(0) 2 Answer: y(t) 5. Find the solution to the following IVP ty -2y - 3t3 cos(4t), y(T/80 Answer: y(t)tsin(4t) 6. Consider the differential equation dy = y(y2-4)(y2 + 9) dt (a) Find the equilibrium solutions of the ODE (b) Construct a phase diagram and determine the stability of the critical points (c) Make rough sketches of typical solution curve:s Answer to a portion of (b): cr.pts. -2-unst. 0-st.2-unst 7. Find the solution to the following IVIP - tan Answer: y(t)-5t tan(t)-5 cos(t 8. Find an explicit expression for the solution y of the following initial value problem 2- y(1) = 2, t-1. 9. A glass of cold soda is placed into a room held at 30 C. (a) If k is a (positive cooling constant), find the differential equation satisfied by the temperature, T (t) of the soda (b) Find the soda temperature as a function of time (and k), if the initial temperature of the soda was 2 C. (c) If after 40 minutes the soda temperature was 10 C, find the cooling constant k nswer: (a) T(T-30): (b) T() 30 - 28e: (e)n(
6 Dec 2022
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Sixta KovacekLv2
24 Aug 2019
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