Differential equations, moneyThe increase of money in your account is proportional to the amount of money that you already have in your account. You deposit $1 per hour into your account. Model this using differential equations.My attempt: y ′ = k y + a where a is the portion of that $1/h. But the question is, how am I supposed to find out the correct portion of that $1/h. That is,how do I find a?

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Differential equations, moneyThe increase of money in your account is proportional to the amount of money that you already have in your account. You deposit $1 per hour into your account. Model this using differential equations.My attempt:      y    ′    =  k  y  +  a where a is the portion of that $1/h. But the question is, how am I supposed to find out the correct portion of that $1/h. That is,how do I find a?

Biardiask3zd · Accepted Answer

Step 1Try thinking about the problem in the case where the interest rate is zero. You get       y    ′    =  a, which has solution   y  =  a  t  +  c. If time is expressed in hours, then you want   a  =  1. (note: make sure you express k using the same units.)Step 2Of course, the typical undergraduate approach isn&#039;t a completely honest representation of the situation. If you&#039;re depositing one dollar an hour you won&#039;t get a nice continuous curve, you&#039;ll have a discontinuous one that jumps every hour.

Differential equations, money. The increase of money in your account is proportional to the amount of money that you already have in your account. You deposit $1 per hour into your account. Model this using differential equations.

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