Mathematics - Differential Equations - Second-order ODEs - Solve Second-Order ODEs

10 problems: (1-2) Distinct real roots: y''-3y'+2y=0, y''+y'-6y=0. (3) Repeated root: y''-4y'+4y=0. (4-5) Complex roots: y''+9y=0, y''+2y'+5y=0. (6-7) Non-homogeneous: y''-y=eˣ (guess y_p=Axeˣ since eˣ is in y_h), y''+y=sin(x). (8) With initial conditions: y''+4y=0, y(0)=1, y'(0)=0. (9) Spring-mass: