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03) Prove or disprove that y = ce* + de ²x is the solution to y(2) + y(¹) - 2y = 0.

03) Prove or disprove that y = ce* + de ²x is the solution to y(2) + y(¹) - 2y = 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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y' - 6x²y + 4xy = y where y(2) - 1 02) Find the orthogonal trajectories for the family of curves given by x²y = k where parameter k is a real number and x and y are variables. 03) Prove or disprove that y = ce + de 2x is the solution to y(2) + y(1) - 2y = 0. 04) A tank contains 3000 liters of water with 500 kilograms of sugar dissolved in it. Water withkg of sugar per liter enters the well mixed solution at the rate of 3 liters per minute. The well mixed solution drains away at 3 liters per minute. Write a fully simplified equation giving the number of kilograms of sugar that are in the tank after t minutes. 05) A loaf of bread is removed from a 450° F oven and is placed to cool in a kitchen having an air temperature of 90° F. After 10 minutes the loaf of bread is 350° F. Write a fully simplified equation giving the temperature of the bread after t minutes. 06) Determine if the sequence converges or diverges. If it converges, find the limit. A₂ = {(²5)"} An n+5 00 8 / 2²²+1 1 T--T Ps W CE (821) at 7
Transcribed Image Text:y' - 6x²y + 4xy = y where y(2) - 1 02) Find the orthogonal trajectories for the family of curves given by x²y = k where parameter k is a real number and x and y are variables. 03) Prove or disprove that y = ce + de 2x is the solution to y(2) + y(1) - 2y = 0. 04) A tank contains 3000 liters of water with 500 kilograms of sugar dissolved in it. Water withkg of sugar per liter enters the well mixed solution at the rate of 3 liters per minute. The well mixed solution drains away at 3 liters per minute. Write a fully simplified equation giving the number of kilograms of sugar that are in the tank after t minutes. 05) A loaf of bread is removed from a 450° F oven and is placed to cool in a kitchen having an air temperature of 90° F. After 10 minutes the loaf of bread is 350° F. Write a fully simplified equation giving the temperature of the bread after t minutes. 06) Determine if the sequence converges or diverges. If it converges, find the limit. A₂ = {(²5)"} An n+5 00 8 / 2²²+1 1 T--T Ps W CE (821) at 7
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