An annuity is a fund into which one makes equal payments at regular intervals. If the fund earns interest at rate r compounded continuously, and deposits are made continuously at the rate of d dollars per year (a continuous annuity), then the value y(t) of the fund after t years satisfies the differential equation  y′ = d + ry.   Solve the differential equation for the continuous annuity y(t) with deposit rate d = $5000 and continuous interest rate r = 0.02, subject to the initial condition y(0) = 0 (zero initial value).   y= ?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.