Dy/dx = 2xy^2 and y(-1) = 2 find y(2)

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—————

Solve the initial value problem:

   dy
———  =  2xy²,      y = 2,  when x = – 1.
   dx

Separate the variables in the equation above:



Integrate both sides:





Take the reciprocal of both sides, and then you have



In order to find the value of  C₁  , just plug in the equation above those known values for  x  and  y, then solve it for  C₁:

y = 2,  when  x = – 1. So,





Substitute that for  C₁  into (i), and you have



So  y(– 2)  is



I hope this helps. =)

Tags:  ordinary differential equation ode integration separable variables initial value problem differential integral calculus

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