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*e1.5x + C2*e-4x , C1 and C2 are real constants.
Answer: C1*e1.5x +C2*e-4x, C1 and C2 are real constants.
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