Hi, Please help me solve the ffg. set of simultaneous equations using D-operators:

dy/dx+2x-3y=1
dy/dx-3x+2y=e^-t

To solve a set of simultaneous equations using D-operators, you can follow these steps:

Step 1: Rewrite the equations in terms of D-operator notation.
- Replace dy/dx with D, which represents d/dx.
- Replace y with y(x) in D-operator notation, which represents the function y(x).

The given equations in D-operator notation are:
D(y) + 2x - 3y = 1 ...(Equation 1)
D(y) - 3x + 2y = e^(-t) ...(Equation 2)

Step 2: Solve for D(y) by rearranging the equations.
- For Equation 1, rearrange it to isolate D(y) on one side:
D(y) = 1 - 2x + 3y

- For Equation 2, rearrange it to isolate D(y) on one side:
D(y) = e^(-t) + 3x - 2y

Step 3: Set the expressions for D(y) equal to each other and solve for y.
1 - 2x + 3y = e^(-t) + 3x - 2y

Step 4: Simplify and solve for y.
Collect like terms:
5y + 5x = e^(-t) + 2
Divide both sides by 5:
y + x = (e^(-t) + 2)/5
Subtract x from both sides:
y = (e^(-t) + 2)/5 - x

Therefore, the solution to the set of simultaneous equations using D-operators is:
y = (e^(-t) + 2)/5 - x