00:01
In this question, we are asked to solve the given initial value problem.
00:04
First, let's separate the variables.
00:06
To do that, we need to multiply both sides by l squared and multiply by dt, then integrate both sides of the equation.
00:19
On the left -hand side, we'll get the integral of l to the negative second power dl, and we'll rewrite the right -hand side.
00:30
Then on the left -hand side, we'll get l to the negative first divided by negative one, and on the right -hand side, to calculate this integral, we'll use integration by parts.
00:41
We'll take u to be ln t and dv to be equal to dt.
00:52
Then du equals to one over t dt and v equals to t.
01:00
Then by the integration by parts formula, we'll get k multiplied by uv minus the integral of vdu.
01:17
This equals to k times t ln t minus t plus the constant of integration c...