(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

y''[x] = y'[x] + x

2. Relevant equations

We were taught two special types of second order diff. equations:

Type 1: Supposed to be when x is missing

v = y'[x]

v'[x] = y''[x]

Type 2: Supposed to be when y is missing

v = y'[x]

v v'[x] = y''[x]

3. The attempt at a solution

The answer key reads:

v'[x] - v = x

d/dx{e^-x v} = x e^-x

e^-x v = C1 * e^-x -x -1

v = C1 * e^x -x -1

y[x] = c2 - c1 * e^-x - (.5)x^2 - x

I don't understand why we used type 1 to solve this problem since x is clearly stated in the problem. I was hoping someone could explain, thanks.

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# Homework Help: Solving a special type of a second order differential equation

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