(Solved): (10 points) (a) Find the general solution of the differential equation \[ y^{\prime \prime}(t)+36 y ...

(10 points) (a) Find the general solution of the differential equation \[ y^{\prime \prime}(t)+36 y(t)=0 \text {. } \] general solution = (Use the letters A and B for any constants you have in your solution.) (b) For each of the following initial conditions, find a particular solution. (i) \( y(0)=0, y^{\prime}(0)=1: y= \) (ii) \( y(0)=1, y^{\prime}(0)=0: y= \) (iii) \( y(0)=1, y(1)=0: y= \) (iv) \( y(0)=0, y(1)=1: y= \) (On a sheet of paper, sketch a graph of the solutions you found in part (b) to see how they differ.)