Question: Problem: A skydiver's position is given by x(t) and is accelerating at the rate x''(t). By Newton's second law, we can infer mx''(t)=a(t)x'(t), where a(t)=1/(t+1)
Problem: A skydiver's position is given by x(t) and is accelerating at the rate x''(t). By Newton's second law, we can infer mx''(t)=a(t)x'(t), where a(t)=1/(t+1) is a function describing the air resistance and m=2 is the skydiver's mass.
a) Find the general solution of this equation, for t is bigger or equal to 0. Hint: can you solve for v=x' first?
b) Find all solutions x(t) satisfying x(0) =2000.
I figured out part a) by using integrating factor and I get 2C1 sqrt(t+1)+C2. For part b, I found the value of x(0) which gave me 2000= 2C1(1)+C2 , which gives 2000-2C1 as my second constant, C2. SO for solution in part b, do I just plug this constant equation in C2? Or is there a way to find a numerical value for the second constant? If then, how can I get both constants in numerical values?
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