# Thread: diffEQ using L, D, Ly, y(x)... not sure how to approach this

1. ## diffEQ using L, D, Ly, y(x)... not sure how to approach this

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

2. Originally Posted by plopony
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