If L = D^2 + 3xD - 4x
and y(x) = 2x - 5e^(2x)
then Ly = ?
This is completely going over my head. I don't know what is being asked. Im not asking someone to solve this for me, just some instruction in how I am supposed to approach this. Thanks
If L = D^2 + 3xD - 4x
and y(x) = 2x - 5e^(2x)
then Ly = ?
This is completely going over my head. I don't know what is being asked. Im not asking someone to solve this for me, just some instruction in how I am supposed to approach this. Thanks
For example if $\displaystyle y=x+\sin(x)$ then
$\displaystyle Ly=(D^2+3xD-4x)(x+\sin(x))$
Now distribute the operator to y to get
$\displaystyle (D^2+3xD-4x)x+(D^2+3xD-4x)\sin(x)$
distributing again gives
$\displaystyle D^2(x)+3xD(x)-4x(x)+D^2(\sin(x))+3xD(\sin(x))-4x(\sin(x))$
Now just take the dervaitves to get
$\displaystyle 0+3x(1)-4x^2-\sin(x)+3x(\cos(x))-4x\sin(x)$
I hope this helps