H2 Maths 5.5 - Differential Equations: Second-Order Linear with Constant Coefficients

What you will learn

• Solve y'' + 3 y' + 2 y = 6 e^x with y(0) = 1 and y'(0) = 0.
• Auxiliary equation m^2 + 3 m + 2 = 0 gives m = -1 and m = -2; complementary function y_c = A e^(-x) + B e^(-2 x).
• Try particular integral y_p = k e^x; substitution gives 6 k e^x = 6 e^x so k = 1, y_p = e^x.