Homogeneous differential equations and Newton's law of cooling

[aparra2]

hey guys i need help with this problem i tried to figure the out but most are homogeneous equations so i don't even know how to start and the Newtons law of cooling i have no idea wut to do .thanks

 

[cristo]

Welcome to the forums aparra2. Firstly, please note that all homework/textbook questions like this should be posted in the homework forums. Also note that you need to show your work before we can help you- forum rules.

For this question, your image is not clear, and I can't quite read the questions. Perhaps you could type the equations out? If you do, then I may be able to give you hints; but are you sure you don't know where to start? What do you know about how to solve these type of equations?

 

[HallsofIvy]

Is the first equation
$$p\frac{dp}{dt}= 1+ x+ 2y+ 2xy$$?
If so, are we to treat y as a constant?

Is the second equation
$$(1+ x^2)\frac{dp}{dx}+ 4xp= \frac{1}{1+x^2}$$?
If so, that is a linear equation. There is a standard formula for finding an "integrating factor". Do you know it?

Is the third equation
$$(p+ t^2y)\frac{dy}{dx}= 2tdt$$?
If so can we treat p as a constant?