anonymous
  • anonymous
If dy/dx = 5x^2y and y(0)=6, find an equation for y in terms of x
Mathematics
chestercat
  • chestercat
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myininaya
  • myininaya
fun we have a function of y times a function of x=y' so we can use separation of variables
myininaya
  • myininaya
so we have dy=5x^2y dx => dy/y=5x^2 dx => integrate both sides: lny=5x^3/3+C
myininaya
  • myininaya
Now if you want to solve y just base e both sides giving you y=e^(5x^3/3+C)

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myininaya
  • myininaya
Ok but we can find C since you are given the initial condition y(0)=6
myininaya
  • myininaya
y(0)=e^(0+C)=e^C=6 => so we have e^C=6 or C=ln6
myininaya
  • myininaya
y=e^(5x^3/3+ln6)
myininaya
  • myininaya
Now wasn't that fun? :)

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