1. Determine whether the sequence of functions sin(x), sin(2x), sin(3x) is linearly independent.

2. Find the general solution of the ODEy5y6y= 0.

3. Find the general solution of the ODEy14y+ 49y= 0.

4. Solve the following IVP:

y16y= 0

y(0) = 1

y(0) = 0

5. Solve the IVP

y^4=y

y(0) = 1

y(0) =2

y(0) = 2

y^3(0) =1

using the information thaty1=e^x,y2=e^x,y3= sinxandy4= cosxare all solutions of the ODEy^4=y.