Write the given differential equation in the form L(y) = g(x), where L is a linear differential operator with constant coefficients. If possible, factor L. (Used for the differential operator.) 3y'' − 8y' − 3y = 4

The complete solution is

Step-by-step explanation:

Given differential equation is

3y"- 8y' - 3y =4

The trial solution is

Differentiating with respect to x

Again differentiating with respect to x

Putting the value of y, y' and y'' in left side of the differential equation

The auxiliary equation is

The complementary function is

y''= D², y' = D

The given differential equation is

(3D²-8D-3D)y =4

⇒(3D+1)(D-3)y =4

Since the linear operation is

L(D) ≡ (3D+1)(D-3)    

For particular integral

       [since ]

         [ replace D by 0 , since L(0)≠0]

The complete solution is

y= C.F+P.I

hd extra 3-7 x d en is the answer