Solving four ODE problems

[prison-rat]

Hi. I have some important questions to solve until tomorrow night..

Can anyone solve them please ?

01
http://img356.imageshack.us/img356/4218/01hz1.jpg

02
http://img356.imageshack.us/img356/4851/02yn6.jpg

03
http://img356.imageshack.us/img356/5762/03pm9.jpg

04
http://img204.imageshack.us/img204/7753/04gr4.jpg



Thank you

 

[tiny-tim]

Welcome to PF!

Hi prison-rat! Welcome to PF!

Show us what you've done and where you're stuck, and then we'll know how to help you!

Start with question 1.

 

[prison-rat]

thanks for your reply.

I solved 1-2 but ımnot sure the re true.
3-4 I am trying
here first 2

http://img514.imageshack.us/img514/3762/answer1rt7.jpg
thanks

 

[HallsofIvy]

You are fine until 2b
$$\int \frac{dy}{1- 2y}\ne ln(1- 2y)+ C$$
Let u= 1- 2y and substitute.

 

[HallsofIvy]

Numbers 3 and 4 look fairly standard. Do you know what an "exact differential" is?

For number 4, notice that there are no odd powers in the characteristic equation.