Solve the differential equation y ' + 5y = 5e x

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Solve the differential equation y ' + 5y = 5e x 1. 2. {image} 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Solve the initial-value problem {image} 1. 2. {image} 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

In the circuit shown in Figure, a battery supplies a constant voltage of 20 V, the inductance is 2 H, the resistance is 10 {image} , and I ( 0 ) = 0. Find the current after 0.9 s. Round your answer to two decimal places. {image} 1.98 A 1.84 A 2.19 A 1.64 A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Let P( t ) be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation {image} as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation. {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s( t ) is the distance dropped after t seconds, then the speed is v = s '( t ) and the acceleration is a = v '( t ). If g is the acceleration due to gravity, then the downward force on the object is mg - pv, where p is a positive constant, and Newton's Second Law gives {image} Find the limiting velocity. {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50