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...(Calculus AB Problems)? 1. Find the solution to the initial value problem:
(e^
+ cosy)y' = x, y(-1) = 0
2. Find the general solution of the differential equation:
(x² + 1)tany(dy/dx) = x, ANS: cosy = c√(x² + 1), correct?
3. Use integration to find a general solution to the differential equation: y' = ((2)/(√(1-x²))) + x
4. Determine which function is a solution to the differential equation: xy' + 2y = 0, ANS: it looks like this
dy/dx = __________
5. The rate of change of y with respect to x is inversely proportional to the square root of y.
a. Write a differential equation for the given statement.
b. Solve the differential equation in part a.
6. Forensics: A murder victim was found at 9 PM. The temperature of the body was measured at 90°F. One hour later the temperature of the body was 89°F. The temperature of the room where the body was found has been maintained at a constant 70°F, and the victim's normal temperature was 98.6°F. Assuming that the temperature "T" of the body obeys Newton's Law of Cooling, write a differential equation for "T" and solve it to estimate the time (to the nearest hour) when the murder occurred.
7. Find the general solution for each d.e.
A. y' = cos x
B. dy/dx = 2x
C. dy/dx = 3x²-3
D. y' = π/2
(e^
+ cosy)y' = x, y(-1) = 02. Find the general solution of the differential equation:
(x² + 1)tany(dy/dx) = x, ANS: cosy = c√(x² + 1), correct?
3. Use integration to find a general solution to the differential equation: y' = ((2)/(√(1-x²))) + x
4. Determine which function is a solution to the differential equation: xy' + 2y = 0, ANS: it looks like this
dy/dx = __________
5. The rate of change of y with respect to x is inversely proportional to the square root of y.
a. Write a differential equation for the given statement.
b. Solve the differential equation in part a.
6. Forensics: A murder victim was found at 9 PM. The temperature of the body was measured at 90°F. One hour later the temperature of the body was 89°F. The temperature of the room where the body was found has been maintained at a constant 70°F, and the victim's normal temperature was 98.6°F. Assuming that the temperature "T" of the body obeys Newton's Law of Cooling, write a differential equation for "T" and solve it to estimate the time (to the nearest hour) when the murder occurred.
7. Find the general solution for each d.e.
A. y' = cos x
B. dy/dx = 2x
C. dy/dx = 3x²-3
D. y' = π/2