Problem

Match the following equations with the differential equations they satisfy.

1.

a.

2.

b.

3.

c.

Solution

For equation 1, we have

Clearly, plugging these derivatives into a and b does not result in a true statement. When we substitute them into equation c, we have

which is true. So 1 is a solution to c.

For equation 2, we have

These derivatives solve equation b:

Finally, 3 should match a.

We see immediately that y'' + y = 0, so 3 is a solution to a.