Re: Solution to Differential equation

charlescalculus_robertobaggio@xxxxxxxxxxx wrote:
Hi, consider the following diff. equation,

dy/dt = gy - k where g= (ln 1.6)/4 and k = 1.2*(10^6)

rearranging, dy/dt - gy = k

Can the method of using an integrating factor be used to solve the
above.

For the integrating factor method, the R.H.S. must be a function of t,
but this time it's a constant, k. Does it still work?

Better, rearrange as:

dt = dy/(g*y - k)

Both sides become integrable:

t = int(y0,yf| 1/(g*y - k) dy)

= ln(y1*g - k)/g - ln(y0*g - k)/g {ln(x) is the natural log}

Solve for y1:

y1 = y0*exp(g*t) - (k/g)*(exp(g*t) - 1)


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