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Initial Value Problems Questions - All Grades

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

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

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

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

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

    The answer is:
    [math]y = x^4 + 15x + 13[/math]
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