SOLUTION: d the specific solution of the differential equation dy/dx= 2y/x^2 with condition y(−2) = e.

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Question 1085511: d the specific solution of the differential equation dy/dx= 2y/x^2 with condition y(−2) = e.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
matrix%281%2C3%2C+dy%5E%22%22%2Fdx%5E%22%22%2C%22%22=%22%22%2C2y%5E%22%22%2Fx%5E2%29

Swap the 2y and the dx

matrix%281%2C3%2C+dy%5E%22%22%2F%282y%5E%22%22%29%2C%22%22=%22%22%2Cdx%5E%22%22%2Fx%5E2%29

integrate both sides












matrix%281%2C3%2Cln%28y%29%2C%22%22=%22%22%2C+-2%2Fx%2B2C%5B1%5D%29%29

Let C = C1

matrix%281%2C3%2Cln%28y%29%2C%22%22=%22%22%2C+-2%2Fx%2BC%29%29

Substitute condition y(-2)=e, which means 

substitute x=-2 and y=e


matrix%281%2C3%2Cln%28e%29%2C%22%22=%22%22%2C+-2%2F%28-2%29%2BC%29%29

matrix%281%2C3%2C1%2C%22%22=%22%22%2C+1%2BC%29%29

matrix%281%2C3%2C0%2C%22%22=%22%22%2C+C%29%29

Substitute C = 0

matrix%281%2C3%2Cln%28y%29%2C%22%22=%22%22%2C+-2%2Fx%29%29

Rewrite as an exponential

matrix%282%2C3%2C%22%22%2C%22%22%2C%22%22%2Cy%2C%22%22=%22%22%2C+e%5E%28-2%2Fx%29%29%29

Edwin