L * di(t)/dt + R₁ * i(t) + R₂ * i(t) + 1/Cq(t) = U

How can I solve the equation with maple if and plot:

L = 2
R₁ = 2
R₂ = 8
C = 1/12
U = 4e^-t 

a) How can i use laplacetransform to solve with maple?

i₁ = i₂ + i₃ 
2i₁ + i₂ + 2i₁ = 30 + 20cos5 + 114sin5  
1/50 i₃ + 4i₃ - 2 i₂ = 0  

i₁(0) = 0

i₂(0)=0

i₃(0)=0

Plot

Hello. I have three diff. equations that I believe I have solved correct. But how do I put this in maple? They must also plotted. Grateful for your help.

1)

y´´ + 2y´ + 2y = 5

Answer: y(x) = C₁ e^-x sinx + C₂ e^-x cosx + 5/2 

Plot.

2)

y´´ + 2y´ + 2y = sin5x

answer: y(x) = sin5/2 + C₁ e^-x

How can I Solve this using maple?

Differential equation:
y(n+2) + 7/10 y(n+1) + 1/10 y(n) = x(n)

x(n) = 1
y(0) = 0
y (1) = 1

Use Z-transformer to define y(n).

Solve y(0), y(1), y(2), y(3) y(4) and y(5) 

Any one?