**Unformatted text preview: **DREXEL UNIVERSITY
Department of Mechanical Engineering & Mechanics
Applied Engineering Analytical & Numerical Methods II
MEM 592 - Winter 2013
HOMEWORK #1: Due Thursday, January 17 @ 630pm 1. [30 points]
/ A. [10] Check if 0 with 2 has a unique solution . B. [10] Show that the general form of the solution of linear ODEs of the form
(1)
is given by
(2)
C. [10] Given the non-linear ODE show how it can be transformed to a corresponding linear one. 2. [30 points]
A. [10] For each of the following ordinary differential equations (ODEs) state and explain: a) the order, b) whether or
not it is linear, c) the unknown function and independent variable, d) whether or not it is homogenous and e)
whether or not it is autonomous.
sin i) 0
tan y ii) 0 B. [10] Check if the suggested functions are solutions to the corresponding ODEs:
i) 2 0 and 2 1 and ii) 1 C. [10] As an object falls in a fluid, its viscosity resists the motion. The equation of motion in this case is
(3)
where denotes the velocity, is the acceleration of gravity and
1 / where and terminal velocity.
3. [40 points]
Solve the following ODEs
i) 2 13 ii)
iii)
iv) 1 0 0. Note that as / the drag coefficient. Show that
(4) increases the velocity approaches a constant value known as ...

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- Spring '14
- ORDINARY DIFFERENTIAL EQUATIONS, Linear ODEs, Applied Engineering Analytical & Numerical Methods II, corresponding ODEs