9 Qs “ODEs of the 1st order”

2018 Fall Semester

ME 501 Mechanical Engineering Analysis Homework 1: ODEs of the 1st 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

 

 

  1. Find integral by the integration by parts

2

I = ƒ x2 cos 2x dx.

0

  1. Find integral by the variable change

1

x2dx

I = ƒ                 .

–1 ƒ1— x2/4

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

Last Updated on February 11, 2019 by Essay Pro