dy a) K3 Solve the differential equation = kyx using the method of separation of variables. dx b) 3 Discuss the difference between the direction fields of the differential equations dy=kyx and dy dx = = -kyx. How the sign of the coefficient affects the solution curves. A racquetball is hit straight upward with an initial velocity of v₁ = km/s. The mass of a racquetball is m=0.05kg. Air resistance acts on the ball with a force numerically equal to Air resistance acts on the ball with a force numerically equal to 0.5v, where v represents the velocity of the ball at time t. To find the velocity of the ball as a function of time and evaluate time for the ball to reach its maximum height w can solve initial value problem using the firs order linear DE such as dv m dt = -0.5vm(9.8), v₁ = k K=3 Rewrite the equation as a standard form of a linear DE. Find the integration factor. d) k= 3 e) Sketch the direction field of the equation from part c) both manually and by using software. Explain the relation between the solution curves and the direction field. K= 3 Find the velocity of the ball as a function of time. How long does it take for the ball to reach its maximum height?

dy a) K3 Solve the differential equation = kyx using the method of separation of variables. dx b) 3 Discuss the difference between the direction fields of the differential equations dy=kyx and dy dx = = -kyx. How the sign of the coefficient affects the solution curves. A racquetball is hit straight upward with an initial velocity of v₁ = km/s. The mass of a racquetball is m=0.05kg. Air resistance acts on the ball with a force numerically equal to Air resistance acts on the ball with a force numerically equal to 0.5v, where v represents the velocity of the ball at time t. To find the velocity of the ball as a function of time and evaluate time for the ball to reach its maximum height w can solve initial value problem using the firs order linear DE such as dv m dt = -0.5vm(9.8), v₁ = k K=3 Rewrite the equation as a standard form of a linear DE. Find the integration factor. d) k= 3 e) Sketch the direction field of the equation from part c) both manually and by using software. Explain the relation between the solution curves and the direction field. K= 3 Find the velocity of the ball as a function of time. How long does it take for the ball to reach its maximum height?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 16E: Find the general solution for each differential equation. Verify that each solution satisfies the...

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