Get Expert Help with Homogeneous Equations and Newton's Law of Cooling

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This discussion focuses on solving homogeneous equations and applying Newton's Law of Cooling. The user, aparra2, expresses difficulty in starting these problems, particularly with the equations presented. Key equations mentioned include p(dp/dt) = 1 + x + 2y + 2xy, (1 + x^2)(dp/dx) + 4xp = 1/(1 + x^2), and (p + t^2y)(dy/dx) = 2tdt. The forum participants emphasize the importance of showing work and suggest using integrating factors for linear equations.

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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
 

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

Is the second equation
[tex](1+ x^2)\frac{dp}{dx}+ 4xp= \frac{1}{1+x^2}[/tex]?
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
[tex](p+ t^2y)\frac{dy}{dx}= 2tdt[/tex]?
If so can we treat p as a constant?
 

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