ian of

Find p(x), q(x) and the general form of

Rivka Thorpe
2020-11-09
Answered

Let ${y}_{1}$ and ${y}_{2}$ be solution of a second order homogeneous linear differential equation ${y}^{\u2033}+p(x){y}^{\prime}+q(x)=0$ , in R. Suppose that ${y}_{1}(x)+{y}_{2}(x)={e}^{-x}$ ,

$W[{y}_{1}(x),{y}_{2}(x)]={e}^{x}$ , where $W[{y}_{1},{y}_{2}]$ is the Wro

ian of${y}_{1}$ and ${y}_{2}$ .

Find p(x), q(x) and the general form of${y}_{1}$ and ${y}_{2}$ .

ian of

Find p(x), q(x) and the general form of

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delilnaT

Answered 2020-11-10
Author has **94** answers

Since

So their linear combinations are also a solution to (*)

Hence

Now,

So, from (*) we have

or

As

Hence,

Now,

As

and

so,

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$f\left(t\right)=10{e}^{-200t}u\left(t\right)$

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The u(t) is what is really confusing me in this problem.

Would it be correct to take out the 10 because it is a constant, find the Laplace transform of

The u(t) is what is really confusing me in this problem.

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