Welcome to Mrs. Young's calculus class blog! Each week, I will start a new post. Students, you can write questions for me or chat with each other about how to solve a particular problem. As part of your class participation grade each week, every student must comment at least once to my post or another student's comment. I look forward to spending this year with you. Enjoy!

Sunday, January 29, 2012

Week 5

We are almost half way through the third quarter! This week we are going to learn one of the most important things in integral calculus: how to solve an integral using u-substitution. This is a slightly different u-substitution than the one we learned with derivatives. Watch the video to the right for a brief explanation. The first person to comment with the correct answer to the integral in the video will receive a couple points extra credit. For your post this week, I'd like you to describe in your own words what the difference is between the general solution and a particular solution to a differential equation.
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13 comments:

  1. Caroline KangJanuary 31, 2012 at 7:48 AM

    A general solution is a solution with constant of integration which can be written C. A particular solution is derived from a general solution with particular value of C.

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  2. AnonymousJanuary 31, 2012 at 9:10 AM

    General solution has the equation with the constant, C, added. Particular solution has a set of limit which allows you to find the exact value

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  3. Alexa SpudieJanuary 31, 2012 at 10:49 AM

    The general solution is the solution with a constant added, C. The particular solution has the constant as a specific quantity as C, the number that satisfies the specifications given.

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  4. Mrs. YoungJanuary 31, 2012 at 10:52 AM

    So far, none of you are really giving me the concept that I was looking for as far as the general solution to a differential equation. You are correct in that we must add the C at the end, but what does that mean?

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  5. aiden wangJanuary 31, 2012 at 11:15 AM

    the general solution is the solution that is used to represent a bunch of graphs which are parallel to each other( parallel doesn't only mean lines,thay can also be curves, even circle). the constant C is just used to show that the graph is not only one. it's like a graph that can move upword or downword along the y-axis instead.

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  6. Mrs. YoungJanuary 31, 2012 at 12:09 PM

    Thank you Aiden. That's more what I was looking for.

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  7. Anna SchrammJanuary 31, 2012 at 12:32 PM

    The general solution is an equation that represents a family of equations by adding a constant C that can represent any constant. The particular solution is the same equation expect with a specific point that it passes through. You can find C by plugging in the x and y coordinates to get a more specific or particular solution.

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  8. Caroline KangJanuary 31, 2012 at 5:35 PM

    I think the answer of the video is [{(3x^2-1)^101]/606}+C]

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  9. Mrs. YoungJanuary 31, 2012 at 5:45 PM

    Good job Caroline. You will get a couple points extra credit!

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  10. Nate LyellFebruary 3, 2012 at 5:43 AM

    A General Solution is the equation that represents all of the possible y values of a certain function, so the general solution will be the same graph only translated up and down the y axis. A particular solution is when you specify a value for the variable C so you can graph a single function.

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  11. christiankFebruary 3, 2012 at 10:27 AM

    The general solution is just the shape of the graph without restrictions. The particular solution is the graph on a particular interval.

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  12. Krista WoodFebruary 4, 2012 at 7:07 PM

    A general solution is the equation that represents all y-values while a particular solution is the graph with a specified interval(C).

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