The general solution of a first-order DE has one arbitrary constant C. An initial condition y($x_0$) = $y_0$ determines C uniquely, giving the particular solution. In JEE, problems often ask: "If y(0) = 1, find y(1)." Strategy: (1) Solve the DE to get y = f(x, C). (2) Substitute x = $x_0$, y = $y_0$ to find C. (3) Substitute C back and evaluate at the desired point. Common pitfall: applying the initial condition BEFORE completing the integration. Always finish the general solution first, then apply the condition. For second-order DEs, you need two conditions (e.g., y(0) = 1 and y'(0) = 2).