Solve the following differential equations using classical methods and the given initial conditions: d²x (a) +6df + 8x = 5 sin 3t, dt² d²x (b) ² + 4x=t², x(0) = 1; dt2 x(0) = 0; x'(0) = 0 x′(0) = 2

Solve the given differential equation by undetermined coefficients. y(x) = 7 y"-9y=(x²-4) sin(3x) - C₁ cos(3x) + C₂ sin(3x) - x³ exp(3x)/4 + (16/37) exp(3x) - x² exp(9x)/4 C₁ exp(-3x) + C₂ x exp(-3x) – x³ sin(6x)/4 + (32/37) sin(6x) – x² cos(6x)/4 exp(-3x) (C₁ sin(3x) + C₂ cos(3x) ) + x² exp(3x)/16 + (37/64) exp(x) C₁ exp(3x) + C₂ x exp(3x) – x² sin(12x)/2 + (31/39) sin(12x) - x² cos(12x)/2 C₁ Cos(3x) + C₂ sin(3x) - x exp(-x)/4 + (33/37) exp(3x) + x² exp(-9x)/4 exp(3x) (C₁ sin(-3x) + C₂ cos(-3x)) + x exp(3x)/16 + (37/64) x² exp(x) C₁ exp(3x) + C₂ exp(-3x) - x² sin(3x)/18+ (37/162) sin(3x) - x cos(3x)/27 0 QUES No solution

Q3/ A: Find General Solutions for the following Differential Equations (Use Differential Operators). (D²+1)y= X² Cos 5X