Science / Solve 5 Calculus Questions

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Can you name the Solve the following differential equations?

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2xy(dy/dx) = y^2 - x^2
no spaces, use k for constant, solve for y 
dy/dx - y = e^(2x)
ditto, use brackets for exponent 
Integrate 1/(1+x^2) dx
ditto, use c for integration constant 
Integrate 1/sqrt(1+x^2) dx
ditto 
Find the closed infinite sum where S=1+1/6+1/36+1/216+...
ditto, write in fractions 

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