Initial Value Problems Questions

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The Initial Value Problems questions below are in the following grade level(s): College
  • Solve y''=12x^2 where y'(0) = 15 and y(0) = 13
    • Itegrate:
      y' = int12x^2dx = 4x^3 + c_1

      Using the first condition y'(0) = 15:
      4(0)^3 + c_1 = 15
      c_1 = 15

      Therefore, the differential equation is:
      y' = 4x^3 + 15

      Integrate again:
      y = int(4x^3 + 15)dx = x^4 + 15x + c_2

      Using the second condition y(0) = 13:
      0^4 + 15*0 + c_2 = 13
      c_2 = 13

      The answer is:
      y = x^4 + 15x + 13