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- #1

I have a question about an example:

"Solve the system:

$x'(t)=3x(t)-4y(t)+1$

$y'(t)=4x(t)-7y(t)+10t$

We write the system using the operator notation:

$(D-3)[x]+4y=1$

$-4x+(D+7)[y]=10t$

We can eliminate x from this system by adding 4 times the first equation to $(D-3)$ applied to the equation. This gives

$(16+(D-3)(D+7))[y]=4*1+(D-3)[10t]=14-30t$"

How does this step work: "We can eliminate x from this system by adding 4 times the first equation to $(D-3)$ applied to the equation."

Thanks

Cbarker1