Ly=y''+py'+qy
Suppose that y1 and y2 are two functions such that:
Ly1=f(x)
Ly2=g(x)
Show that their sum y=y1+y2 satisfies Ly= f(x)+g(x)

Question

Ly=y''+py'+qy
Suppose that y1 and y2 are two functions such that:
Ly1=f(x)
Ly2=g(x)
Show that their sum y=y1+y2 satisfies Ly= f(x)+g(x)

abb0t · Answer

@OrthodoxMan

anonymous · Answer

I'm too tired 
off to bed 
this is yours my king @abb0t

anonymous · Answer

?

zepdrix · Answer

Hmm, not sure what they're asking for here.
Lemme share what I'm thinking...$$\Large\rm Ly=y''+py'+qy$$Then plugging in y_1 for our y gives us,$$\Large\rm Ly_1=y_1''+py_1'+qy_1$$Which we can write as,$$\Large\rm f(x)=y_1''+py_1'+qy_1$$

zepdrix · Answer

We can do similarly with the g(x) information, yah?
And then just add some stuff up to show linearity.

zepdrix · Answer

$$\Large\rm g(x)=y_2''+py_2'+qy_2$$

$$\Large\rm f(x)+g(x)=...$$

zepdrix · Answer

From there it's just a matter of grouping things up.
What do you think miss Brittni? :)

anonymous · Answer

I think you're right.

anonymous · Answer

I just wasnt sure what was being asked.