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# 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

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