particular solutions, boundary conditions, falling object

baja44

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Joined
Nov 4, 2007
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1
I have 3 problems I cannot understand at all:

1. Find the particular solution of the differential equation that satisfies the boundary condition: xdy=(x+y+8)dx; y(1)=3

2. Find the particular solution of the differential equation that satisfies the boundary condition: 5xy'-y=x^3-5x; y(squareroot of 35/2)=0

3. Assume an object weighing 8 pounds is dropped from a height of 8,000 feet, where the air resistance is proportional to the velocity.
a) Write the velocity as a function of time if its velocity after 4 seconds is 2.00 feet per second.
b) What is the limiting value of the velocity function?
 
1. Solve for y' and consider the derivative of y/x.
2. Turn this into a first order linear equation (divide by 5x).
3. Use free fall equation with added term for air resistance.
 
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