Sp2016 Practice Exam 3:  
Name_________________

Show polynomials etc. you enter in calculators and explain what you did. 
No imaginary numbers in final answers.
Read the instructions. I am frequently trying to save you time. 
Use the back of a page to show more work if you need to.
4 questions - 25 points each.

Solve y''+ 4 y' +4y= 48 (e^(2t))               with y[0]=4, y'[0]=8

y[x]/.DSolve[ {y''[x]+ 4 y'[x]+4 y[x]==48 (E^(2 x)),y[0]==4,y'[0]==8},
y[x],x][[1]]//Expand//TraditionalForm

Solve y''+2 y'+5 y= 50t+ 17 sin(2t)

DSolve[y''[t]+2 y'[t]+5 y[t]==50t+17 Sin[2 t],y[t],t][[1]]//Simplify

({{ Q1     ,    Q2   ,    Q3   ,    Q4   ,    Total   }, {      ,       ,       ,       ,       }})

Solve y''' + 3 y'' + 3 y' + y = 6(e^(-t))

Simplify[ y[t]/.DSolve[ y'''[t]+ 3 y''[t] + 3 y'[t]+y[t]==6(E^(-t)), y[t],t][[1]] ]//Expand

({{Score/25}, {      }})

Show that (Subscript[y, 1])=(t^(-2)) is a solution of  (t^2)y''+5 t y'+4y= 0.

Solve (t^2)y''+5 t y'+4y= 50(t^3).
Make sure you write down equations you are solving and explain your process and steps.

DSolve[ (t^2)y''[t]+ 5 t y'[t]+4 y[t]==50(t^3), y[t],t]

({{Score/25}, {      }})