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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Note k is 3. differential equation
Transcribed Image Text: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?
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