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Solve the differential equation with constant coefficients
- Thread starter Fatima Hasan
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In summary, a differential equation with constant coefficients has all of its coefficients as constants. The general method for solving these equations involves rearranging and using techniques such as separation of variables, integration, or substitution. However, some equations may require more advanced techniques or special methods. There are also special cases to consider, such as when the coefficients are complex or when there are repeated roots. To check the accuracy of a solution, one can substitute it back into the original equation or graph it and compare it to the graph of the original equation.
- #2
mjc123
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How do you get √56? Shouldn't it be (√52)/4 = (√13)/2?
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mjc123
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Looks OK to me.
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Mark44
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1. In the future, please post questions about differential equations in the Calculus & Beyond section. I will move the ones you have posted in the Precalc section.Fatima Hasan said:
2. You don't need to ask us to check your work for these kinds of problems. Just substitute your solution in the original diff. equation.
Related to Solve the differential equation with constant coefficients
1. How do I identify a differential equation with constant coefficients?
A differential equation with constant coefficients is one in which all of the coefficients are constants, meaning they do not contain any variables. For example, y'' + 3y' + 2y = 0 is a differential equation with constant coefficients, as all of the coefficients (1, 3, and 2) are constants.
2. What is the general method for solving a differential equation with constant coefficients?
The general method for solving a differential equation with constant coefficients is to first rearrange the equation so that all of the derivatives are on one side and the remaining terms are on the other side. Then, you can use techniques such as separation of variables, integration, or substitution to solve for the unknown variable.
3. Can I use the same method to solve all differential equations with constant coefficients?
While the general method for solving differential equations with constant coefficients can be applied in many cases, some equations may require more advanced techniques or special methods. It is important to carefully examine each equation and choose the appropriate method for solving it.
4. Are there any special cases for solving differential equations with constant coefficients?
Yes, there are a few special cases that may arise when solving differential equations with constant coefficients. These include when the coefficients are complex numbers, when there are repeated roots, and when the coefficients are equal to zero. Each of these cases may require a slightly different approach in solving the equation.
5. How can I check the accuracy of my solution for a differential equation with constant coefficients?
One way to check the accuracy of your solution for a differential equation with constant coefficients is to substitute it back into the original equation and see if it satisfies the equation. Additionally, you can also graph the solution and compare it to the graph of the original equation to visually confirm its accuracy.
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