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Check general solution to ODE please!

  1. Mar 1, 2012 #1
    Ok I'm new to ODE's so yeh, just to double check heres what ive done:

    Question: Find the general solution to the following differential equation:
    Equation: y'(x) = sec2 (3x + 1)

    My answer: Don't I just integrate? So dy/dx = sec2 (3x + 1)

    then, y = sec2 (3x + 1) dx

    so y = (tan(3x+1))/3
     
  2. jcsd
  3. Mar 1, 2012 #2

    HallsofIvy

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    Why not check it yourself- differentiate that function!
     
  4. Mar 1, 2012 #3

    don't forget +C
     
  5. Mar 2, 2012 #4
    Ah of course, thanks =)
     
  6. Mar 2, 2012 #5
    I wasn't worried as to whether my integration was wrong I was worried as to whether my methodology was wrong or not.
     
  7. Mar 2, 2012 #6
    Yes, you are correct but what he said will help verify wether your methodology is correct or not, because an appropriorate one would of course lead to the correct solution :)

    as a rule of thumb:

    when y=sec2(αx+b) and you want to find the integral:

    then ∫sec2(αx+b)dx = 1/α*tan(αx+b)
     
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