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Homework Help: Does this method make sense written down this way?

  1. Dec 10, 2011 #1
    1. The problem statement, all variables and given/known data

    Solve the differential equation: [tex]\frac{d^2y}{dx^2}=3x^2-10x+3[/tex]

    3. The attempt at a solution

    [tex]\int\int \frac{d}{dx}\frac({dy}{dx})3x^2-10x+3=\frac{1}{4}x^4-\frac{5}{3}x^3+\frac{3}{2}x^2+c[/tex]

    Does that make sense mathematically?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 10, 2011 #2

    SammyS

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    No. Not even if you fix the parentheses.

    [itex]\displaystyle\int\frac{d}{dx}\left(\frac{dy}{dx} \right)dx=\int\left(3x^2-10x+3\right)dx[/itex]

    [itex]\displaystyle\frac{dy}{dx}=x^3-5x^2+3x+C_1[/itex]

    So that: [itex]\displaystyle y=\int\left\{\int\frac{d}{dx}\left( \frac{dy}{dx} \right)dx\right\}dx=\int\left(x^3-5x^2+3x+C_1\right)dx[/itex]
    which has an additional constant of integration.​
     
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