Answer to Question #89427 in Differential Equations for adigam amos jacob

Question

solve the differential equation 2d^2y/dx^2+5dy/dx-12y=0

Answer 1

Characteristic equation for given equation is

2t² + 5t - 12=0

D = 5²-4*2*(-12) = 121 = 11²

roots t₁= (-5+11)/(2*2) = 6/4 = 1.5, t₂ = (-5-11)/(2*2) = -4

Roots of characteristic equation are real and distinct, then general solution has the form

C₁*e^1.5x + C₂*e^-4x , C₁ and C₂ are real constants.

Answer: C₁*e^1.5x +C₂*e^-4x, C₁ and C₂ are real constants.