The difference equation 2.5(y(t)-y(t-1))=0.1y(t) has a general solution of y(t)=8(1.04)^t, thus with y(0)=8 the particular solution is y(t)=8(1.04)^t.

If I run the problem with Maple, I get exactly the expected answer. However, if I run the problem in Mathematica, I get a wrong answer:

RSolve[2.5 (y[t] – y[t – 1]) == 0.1 y[t], y[t], t]

{{y(t)→c10.961.−1.t}}

\left\{\left\{y(t)\to c_1 0.96^{1.\, -1. t}\right\}\right\}

With the particular solution

RSolve[{2.5 (y[t] – y[t – 1]) == 0.1 y[t], y[0] == 8}, y[t], t]

{{y(t)→8.0.96−1.t}}

\left\{\left\{y(t)\to 8. 0.96^{-1. t}\right\}\right\}

Which is not the expected answer. What am I doing wrong here?

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As it happens, the “correct” answer and Mathematica’s evaluate to approximately the same results. I still cannot explain the difference in the solutions.

– team-rf

Mar 9 at 19:47

2

0.96−1≈1.040.96^{-1} \approx 1.04…

– Marius Ladegård Meyer

Mar 9 at 19:47

1

And if you replace 2.5 by 25/10 and 0.1 by 1/10 you get exact coefficients.

– Marius Ladegård Meyer

Mar 9 at 19:51

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1 Answer

1

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As it turns out, both answers are correct. This is mathematica’s answer when using rational numbers:

{{y(t)→81−t(253)t}}

\left\{\left\{y(t)\to 8^{1-t} \left(\frac{25}{3}\right)^t\right\}\right\}

Maple’s answer is

t→8(2524)t

t\rightarrow 8 \left(\frac{25}{24}\right)^t

Mathematica’s is more complex, but correct after all.