Question

solve (D^2+3D+2)y=0 ​

Answer 1

Answer:

Given differential equation is

(D² - 3D + 2)y = 0

Auxiliary equation of above differential equation is

D² - 3D + 2 = 0

=> D² - 2D - D + 2 = 0

=> D(D - 2) - 1(D - 2) = 0

=> (D - 2)(D - 1) = 0

=> D = 2,1

Hence the general solution is given by

y = c₁e²ˣ + c₂eˣ

Answer 2

Given,

A differential equation (D²+3D+2)y = 0

To Find,

The solution of this differential equation.

Solution,

The given differential equation is

(D² +3D + 2)y = 0

Now, The auxiliary equation of above differential equation is

D² + 3D + 2 = 0

D² + 2D + D + 2 = 0

D(D + 2) + 1(D + 2) = 0

(D + 2)(D + 1) = 0

D = -2 or -1

Now, the general solution is given by

y = c₁e⁻²ˣ + c₂e⁻ˣ

Hence, the general solution of the differential equation is y = c₁e⁻²ˣ + c₂e⁻ˣ.