Solve the differential equation dy/dx= 2y for y given that when x = 1, y = 1

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- Jan 15th 2010, 09:31 PMdifferentiatesolve the differential equation
Solve the differential equation dy/dx= 2y for y given that when x = 1, y = 1

Thanks - Jan 15th 2010, 09:54 PMCalculus26
1. separate the variables

dy/y = 2dx

2. integrate

ln|y| = 2x+ c

3. Apply ICs x= y = 1

0 = 2 + c

c=-2

ln|y| = 2x - 2

4. exponentiate

y = e^(2x-2) = e^(-2) e^(2x) - Jan 15th 2010, 09:57 PMProve It