Differential Equations Question

DIFF EQ HW 6 1. Newtons Law of Cooling: A textbook is left overnight in the trunk of a car during winter, and it reaches a temperature of 10◦ F. The book is then brought into a room that is 72◦ F, and after 10 minutes the book has reached a temperature of 40◦ F. What is the books temperature 1 hours after it was brought into the room? 2. Newton’s Law of Cooling: A calculator at 74◦ F is placed int he trunk of a car where the temperature is only 20◦ F. The calculators temperature decreases 2◦ F after 1 minute. When will the calculators temperature drop to 32◦ F? 3. Newton’s Law of Cooling: A laptop at 70◦ F is placed inside an enclosed car where the temperature is 160◦ F. The laptop’s temperature increases by 30◦ F after 7 minutes. (a) What will the laptop’s temperature be after 1 hour after it is placed in the car? (b) If the laptop can only sustain a maximum temperature of 120◦ , when will the laptop be damaged by the heat? 4. Method of Undetermined Coefficients Without solving the differential Equation, apply undetermined coefficients to determines the simplest form of the particular solution to thew given differential Equation. (a) y ′′ − 16y = sin(4x) + x + 1 (b) y ′′ + 4y = e2x + x2 (c) y ′′ + 4y = 10×2 + 1 5. Solve the given differential equation using the Method of Undetermined Coefficients: (a) y ′′ + 3y ′ + 2y = 6 (b) y ′′ − 10y ′ + 25y = 30x + 3 (c) y ′′ + 4y = 3 sin(2x) 6. Solve the given Initial Value Problem using the Method of Undetermined Coefficients: (a) y ′′ + 4y = −2, y(π/8) = 1/2, y ′ (π/8) = 2 (b) 5y ′′ + y ′ = −6x, y(0) = 0, y ′ (0) = −10 1