Need help solving differential equation?

Solve the differential equation, and find the constant of integration: y' = 3x^2 + 5 and the curve passes through the point (1,8).

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  • hfshaw
    Lv 7
    7 years ago
    Favorite Answer

    You have:

    y' = dy/dx = 3x^2 + 5

    This is a separable equation:

    dy = (3x^2 + 5) dx

    Integrate both sides:

    y(x) = x^3 + 5x + c

    where c is the combined constant of integration.

    Now use the fact that y(x) passes through (1,8) to determine the value of the constant.

    y(1) = 8 = 1 + 5 + c

    c = 2

    So the particular solution for this case is:

    y(x) = x^3 + 5x + 2

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