2018 Fall Semester

ME 501 Mechanical Engineering Analysis **Homework 1**: ODEs of the 1^{st} order Assigned: 8/23/2018

Due: 9/04/2018

For every problem 3 – 9,

- Find the general solution of the
- Substitute the general solution into equation and check that the solution turns the equation into
- If the initial condition is given, find the particular

- Find integral by the integration by parts

2

I = ƒ x2 cos 2x dx.

0

- Find integral by the variable change

1

x2dx

I = ƒ __ __.

–1 ƒ1— x2/4

- yu= e2s–1y2, y(0.5) = 0.5.
- yu = ƒy–2— 1, y(0) = 1.
- xyu = y + 3×4 cos2(y/x) , y(1) = 0 (solve as separable after a variable change).
- yu +y sin x = ecoss , y(0) = —2.5.
- xyu = 2y + x3es.
- yu— y tan x = sin x , y(0) = 1.
- yu+ x2y = y2 (Solve as the Bernoulli equation).