General Solution

General Solution Of Equation (1), Definite Integral Form

By taking t = a in the above equation, we find that C = y(a). Thus the particular solution of equation (1) with the initial condition y(a) = y₀ is obtained by replacing C by y₀. This formula is useful when one or both of the integrals cannot be evaluated. In a simple problem, it is better to use Steps 1 to 4, which break the solution process into smaller parts.

In the following example, we are able to evaluate the first integral but not the second, so the solution is left in a form with one definite integral.

Example 4

Example 5