Differential Equations

[stone badge]

so

[stone badge]

how do I solve an equation that looks like this

$f''(x)-f(x)=0$

[agile shard]

آدم

[nocturne forge]

Do you know what f(x) is?

[stone badge]

no, it's a differential equation

[dusk anvil]

I'm not sure how to hint at what the solution is without spoiling it... It's a second-order linear ODE; for all of them the (basis) solutions are of the form ||e^(λ x)||, and in this case λ can only have two possible values.

[stone badge]

i got lambda = +-1 @dusk anvil

[dusk anvil]

yeah. so you have two basis solutions. since this is a linear ODE, the general solution is an arbitrary linear combination of them.

[stone badge]

what is the general solution?