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calculus

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how do you solve the initial value problem by using separation of variables dy/dx=1+x/(sqrt of y), y(2)=9

  • calculus (()) - ,

    Watch missing parentheses, please.

    Parentheses are needed to enclose numerators and denominators, otherwise additions and subtractions will take place after the division.

    Separate the variables,
    dy/dx = (1+x)/sqrt(y)
    sqrt(y)dy = (1+x)dx
    Integrate:
    (2/3)y^(3/2) = x + x²/2 + C
    y = [(3/2)(x+x²/2+C)]^(2/3)
    from which we can solve for C=14.
    so
    y(x)=[(3/2)(x+x²/2+14)]^(2/3)

    Please check all arithmetic.

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