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I recently solved (non-numerically) the differential equation of the simple pendulum problem,

$$y''=-c*\sin(y)\tag{1}.$$

I then tried to solve the equation with drag. I failed. I don't want to solve it numerically because I'm doing this for fun and that would be fun, $$y''=-c*sin(y)-a*y'\tag{2}.$$

So how would I go about adding drag to $y$ ad hoc, or without actually solving the second differential equation?

The constants of $y$ in my solution shift the equation along the $x$-axis and change the slope at $y(x)=0$ & $|y'(x)|=y'(x)$.

I recently solved (non-numerically) the differential equation of the simple pendulum problem,

$$y''=-c*\sin(y)\tag{1}.$$

I then tried to solve the equation with drag. I failed. I don't want to solve it numerically because I'm doing this for fun and that would be fun, $$y''=-c*sin(y)-a*y'\tag{2}.$$

So how would I go about adding drag to $y$ ad hoc, or without actually solving the second differential equation?

The constants of $y$ in my solution shift the equation along the $x$-axis and change the slope at $y(x)=0$ & $|y'(x)|=y'(x)$.

If you give me an equation of how the amplitude should change over time that would also work since the slope and amplitude are directly related.

I recently solved (non-numerically) the differential equation of the simple pendulum problem,

$$y''=-c*\sin(y)\tag{1}.$$

I then tried to solve the equation with drag. I failed. I don't want to solve it numerically because I'm doing this for fun and that would be fun, $$y''=-c*sin(y)-a*y'\tag{2}.$$

So how would I go about adding drag to $y$ ad hoc, or without actually solving the second differential equation?

The constants of $y$ in my solution shift the equation along the $x$-axis and change the slope at $y(x)=0$.

I recently solved (non-numerically) the differential equation of the simple pendulum problem,

$$y''=-c*\sin(y)\tag{1}.$$

I then tried to solve the equation with drag. I failed. I don't want to solve it numerically because I'm doing this for fun and that would be fun, $$y''=-c*sin(y)-a*y'\tag{2}.$$

So how would I go about adding drag to $y$ ad hoc, or without actually solving the second differential equation?

The constants of $y$ in my solution shift the equation along the $x$-axis and change the slope at $y(x)=0$ & $|y'(x)|=y'(x)$.