How to solve a differentialble equation by separating the variables

The video tutorial explains solving a differential equation by separating variables, integrating, and finding a particular solution. The instructor demonstrates the process of moving terms to isolate variables, integrating both sides, and solving for constants using given points. The tutorial concludes with verifying the solution by plugging values back into the equation.

Describe how to verify if a solution satisfies the original equation.

What is the significance of the negative square root in the context of the problem?