Final answer:
To solve a differential equation, one must identify known and unknown quantities, select the appropriate equation(s), substitute the known quantities with units to find the numerical solution, and verify the solution for correctness and reasonableness.
Step-by-step explanation:
When solving a differential equation, you need to follow a series of steps to find the exact solution. First, you need to identify the knowns and unknowns within the problem. With this information, you can then find an equation or set of equations that will help to solve for the unknowns. It is important to use equations that minimally contain unknown variables; however, if multiple unknowns are present, additional equations will be necessary.
Once the appropriate equations are identified, it's crucial to substitute the known quantities along with their units into the chosen equation to obtain a numerical solution that includes units. This substitution should be checked thoroughly to ensure accuracy.
After finding the solution, it's essential to verify that it is correct by checking if the numbers are reasonable and if the units are consistent. For differential equations, often a derivation or verification is performed by taking the derived variable (such as the first and second derivatives) and substituting them back into the original equation to confirm that the solution satisfies the equation.