# Linear Differential Equations and Linear Operator Problem

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1. Oct 22, 2016

### whitegirlandrew

1. The problem statement, all variables and given/known data
I'm not sure how to approach this. The question involves linear operators and a non-homogenous differential equation.
Here is the question:
https://s15.postimg.org/cdmw80157/Capture.png

2. Relevant equations
They are given in the question

3. The attempt at a solution
I really have no idea on how to approach it. I was thinking something along the lines of setting c1*y1+c2*y2+c3*y3 as a linear combination and setting them equal to the non-homongenous term g(x). Then i can find the values of c1,c2,c3.

2. Oct 22, 2016

### LCKurtz

[Edited] You want to take a linear combination of the $L(y_i)$'s (the right hand side of the equations) equal to $g(x)$, not the $y_i$'s themselves. Then use your constants to build the particular solution from the $y_i$'s.

Last edited: Oct 22, 2016
3. Oct 22, 2016

### whitegirlandrew

I did L(c1y1+c2y2+c3y3)=g(x)=c1*L(y1)+c2*L(y2)+c3*L(y3)
Then I sub in the L(y1), L(y2), and L(y3) for what was given to me. This leads me to find the constants. Then c1=10/12, c2=0, and c3=5/6.
However this was wrong.

4. Oct 22, 2016

### LCKurtz

I corrected my reply while you were looking at it. Sorry. See if it makes sense now.

5. Oct 22, 2016

### whitegirlandrew

Ah I see. I got the question wrong so I don't know the answer. I will try this once the solution comes out. Thanks for the help.

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