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(dy)/(dx) = (x-2) e^(-2y) and
y(2)=ln2 what is y(x)?

User Ospr
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1 Answer

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(dy)/(dx) =(x-2)e^(-2y)

\int e^(2y) dy = \int (x-2)dx

(1)/(2) e^(2y)= (1)/(2) x^2-2x+c
given y(2) = ln 2:
(1)/(2) e^(2\ln2)= ((1)/(2) * 2^2)-(2*2)+c

2=2-4+c \therefore c=4

(1)/(2) e^(2y)= (1)/(2) x^2-2x+4

e^(2y)=x^2-4x+8

2y=\ln(x^2-4x+8)

y(x)= (1)/(2) \ln(x^2-4x+8)
User Michaelmesser
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