Query 07

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course MTH 279

2:33 pm 2/28

Query 07 Differential Equations

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Question:  3.4.2.  Solve the equation y ' = 2 t y ( 1 - y), with y(0) = -1, as a Bernoulli equation.

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Your solution: 

v = y^(1-n)= y^-1

v' + (-1)2tv = -2t

I= e^-t^2

e^(-t^2)*v = int(-2te^(-t^2)) = e^-t^2

v = 1 + Ce^(t^2)

y= v^(1/-1) = v^-1

y = (1+Ce^(t^2))^-1

y = 1/(1+Ce^(t^2))

y(0)= - 1 --> C = -2

y = 1/(1-2e^(t^2))

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Given Solution: 

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