Question

Find the general solution of the following differential equations
12y"-5y' - 2y = 0

Answer 1

Corresponding (auxiliary) equation

$$12r^2-5r-2=0$$

$$d=(-5)^2-4(12)(-2)=121$$

$$r=\dfrac{5\pm\sqrt{121}}{2(12)}=\dfrac{5\pm11}{24}$$

$$r_1=\dfrac{5-11}{24}=-\dfrac{1}{4},r_2=\dfrac{5+11}{24}=\dfrac{2}{3}$$

The general solution of the given differential equation is

$$y(t)=c_1e^{-{1 \over 4}t}+c_2e^{-{2 \over 3}t}$$