Please check my work (find general solution of DE)

In summary, the general solution for the given equation is y = c_1e^-2x + c_2e^-x, with characteristic roots r = -2 and r = -1.
  • #1
darryw
127
0

Homework Statement


"find the general solution of the equation: y'' + 3y' + 2y = 0

characteristic is:
r^2 + 3r + 2 = 0

solve quadratic:
(r+2)(r+1)

r = -2
r= -1

therefore GS of equation is: y = c_1e^-2x + c_2e^-x

thanks for any help

Homework Equations


The Attempt at a Solution

 
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  • #2
darryw said:

Homework Statement


"find the general solution of the equation: y'' + 3y' + 2y = 0

characteristic is:
r^2 + 3r + 2 = 0

solve quadratic:
(r+2)(r+1)

r = -2
r= -1

therefore GS of equation is: y = c_1e^-2x + c_2e^-x

thanks for any help
This is easy enough to check. For you solution, it should be that y'' + 3y' + 2y = 0. If so, your solution is correct.
 

1. What is a "general solution" of a differential equation?

A general solution of a differential equation is a function that satisfies the equation for all possible values of the independent variable. It contains a constant of integration and represents the family of all possible solutions to the equation.

2. How do you find the general solution of a differential equation?

To find the general solution of a differential equation, you will need to integrate the equation and include a constant of integration. The number of constants of integration will depend on the order of the differential equation. For example, a first-order differential equation will have one constant, while a second-order equation will have two.

3. What is the difference between a general and a particular solution?

A general solution is a function that represents all possible solutions to a differential equation, while a particular solution is a specific function that satisfies the equation for given initial conditions. A particular solution can be obtained from a general solution by substituting the initial conditions into the equation and solving for the constants of integration.

4. Can you check my work for finding the general solution of a differential equation?

Yes, as a scientist, I can check your work and provide feedback on your solution to a differential equation. However, it is important to note that there may be multiple ways to arrive at the general solution, so my feedback may vary depending on the method you used.

5. Are there any tips or tricks for finding the general solution of a differential equation?

One helpful tip is to always check your solution by differentiating it and plugging it back into the original equation. This will ensure that your solution is valid and satisfies the equation. Additionally, understanding the properties and techniques of integration can also be useful in finding the general solution of a differential equation.

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