Bill Goodwine's Courses

Reading: Chapter 3.

Exercises: 2.9, 2.10 (9, 10 and 11 only), 2.14, 2.19, 2.21, 2.22 and 2.25 (2, 4, 6 and 8 only).

For linear first order differential non homogeneous equations with variable coefficients are there two different methods that you can use to find the general solution? (Problem 2.21) I know that you can use variation of parameters but undetermined coefficients does not work. Thanks

Jessie wrote:For linear first order differential non homogeneous equations with variable coefficients are there two different methods that you can use to find the general solution? (Problem 2.21) I know that you can use variation of parameters but undetermined coefficients does not work. Thanks

The methods for nonlinear first order (separable or exact) may work even though the equation is linear.

Jessie wrote:For linear first order differential non homogeneous equations with variable coefficients are there two different methods that you can use to find the general solution? (Problem 2.21) I know that you can use variation of parameters but undetermined coefficients does not work. Thanks

I thought the same thing at first, but undetermined coefficients will work if you get the original equation in the right form before you start it.

sschwane wrote:

Jessie wrote:For linear first order differential non homogeneous equations with variable coefficients are there two different methods that you can use to find the general solution? (Problem 2.21) I know that you can use variation of parameters but undetermined coefficients does not work. Thanks

I thought the same thing at first, but undetermined coefficients will work if you get the original equation in the right form before you start it.

I don't see how you can convert it to a constant coefficient equation so that undetermined coefficients works, so in general that will not be a viable approach for this type of equation. However, there is no point in being too formalistic, and if you found a way that gives the right solution, then it's ok.