- #1
Jeff12341234
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I'm not sure if my answer is correct. Did I make a mistake somewhere? I'm not sure the ± needs to be there.
Correcting Mistakes in Representing Constants for a Differential Equation?
- Thread starter Jeff12341234
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In summary, the conversation discusses finding a quadratic equation through a series of equations involving derivatives and constants. The main focus is on determining the values of the constants c1 and c2 through linear equations. The conversation also addresses a mistake made in the original calculation.
- #2
HallsofIvy
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How in the world did you get a quadratic equation out of this? [itex]y(2)= (C_1+ 6C_2)e^6= e^6[/itex] and [itex]y'(1)= (3C_1+ 4C_2)e^3= e^3[/itex]. The derivative is [itex]y'= 3C_1e^{3x}+ C_2e^{3x}+ 3C_2xe^{3x}= ([3C_1+ C_2]+ 3C_2x)e^x[/itex]. It does not involve "[itex]C_1C_2[/itex]"!
You have [itex]C_1+ 6C_2= 1[/itex] and [itex]3C_1+ 4C_2= 1[/itex], two linear equations.
You have [itex]C_1+ 6C_2= 1[/itex] and [itex]3C_1+ 4C_2= 1[/itex], two linear equations.
- #3
Jeff12341234
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c1 is represented by c, c2 is represented by d
That's y'
I did make an error by leaving out the + sign between c1 and c2 for y'
That makes c1 = -1 and c2 = 1
That's y'
I did make an error by leaving out the + sign between c1 and c2 for y'
That makes c1 = -1 and c2 = 1
Last edited:
Related to Correcting Mistakes in Representing Constants for a Differential Equation?
1. What is a "D.E.: Boundary Value Problem"?
A "D.E.: Boundary Value Problem" refers to a type of problem in mathematics and physics that involves solving a differential equation (D.E.) subject to certain boundary conditions. These boundary conditions specify the values of the solution at the boundaries of the domain in which the D.E. is being solved.
2. How is a "D.E.: Boundary Value Problem" different from an "I.V.P."?
A "D.E.: Boundary Value Problem" is different from an "I.V.P." (initial value problem) in that an I.V.P. only specifies the value of the solution at one point, while a B.V.P. specifies the values at multiple points. Additionally, an I.V.P. typically involves solving the D.E. over a specific interval, while a B.V.P. involves solving the D.E. over a specific domain.
3. What are some real-world applications of "D.E.: Boundary Value Problems"?
"D.E.: Boundary Value Problems" have numerous applications in fields such as physics, engineering, and economics. For example, they can be used to model heat transfer in a material, the flow of fluids in pipes, and the behavior of a financial market.
4. What are some common techniques for solving "D.E.: Boundary Value Problems"?
Some common techniques for solving "D.E.: Boundary Value Problems" include using numerical methods such as finite difference or finite element methods, as well as analytical methods such as separation of variables or Laplace transforms. The specific method used depends on the complexity of the problem and the desired level of accuracy.
5. How can "D.E.: Boundary Value Problems" be useful in understanding physical phenomena?
"D.E.: Boundary Value Problems" can be useful in understanding physical phenomena because they allow us to model and analyze systems that are governed by differential equations. By solving these problems, we can gain insights into the behavior of these systems and make predictions about how they will evolve over time.
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