If I have an equation in the form: dy/dx + f(x)y = g(x)
How can it be solved as y = e^-w * (integral (g(x)*e^w dx) + k) ?
To make it simpler, g(x) = 0, which would make it:
y = e^-w * k
But I still don't see how you arrive at this formula.
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If I have an equation in the form: dy/dx + f(x)y = g(x)
How can it be solved as y = e^-w * (integral (g(x)*e^w dx) + k) ?
To make it simpler, g(x) = 0, which would make it:
y = e^-w * k
But I still don't see how you arrive at this formula.
Just to be clear, w = integral f(x) dx
Seems to work. If g(x) = 0 then:
If, then substituting in the above yields:
We can substitute forto get:
, as expected.
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