Asked by mabel
find a function f given that (1) the slope of the tangent line to graph of f at any point P(x,y) is given by dy/dx=3xy and (2) the graph of f passes through the point (0,2)
Answers
Answered by
Steve
dy/dx = 3xy
dy/y = 3x dx
ln y = 3x^2/2+c
y = Ce^3x^2/2
2 = Ce^0
C = 2
y = 2e^(3x^2/2)
y' = 2e^(3x^2/2)*(3x)
= 3xy
dy/y = 3x dx
ln y = 3x^2/2+c
y = Ce^3x^2/2
2 = Ce^0
C = 2
y = 2e^(3x^2/2)
y' = 2e^(3x^2/2)*(3x)
= 3xy
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