MA 238-02
§3.7 + handouts Quiz #5 score
Name:
5 April 1999
1. Determine the largest interval in which the IVP has a unique solution. You need not find
the solution but you should explain how you arrive at your conclusion.
t(t −4)y +3ty+4y=2,y(3)=0,y
(3)=−1
2. Compute the Wronskian of the two functions y1=t2and y2=y3. Is it possible for
{t2,t3}to be a basic set of solutions for a differential equation of the form y +a(t)y +
b(t)y =f(t) on the interval I=(−1,1). Assume that a(t ), b(t), f (t) ∈C0(I).
3. Use variation of parameters to find a particular solution for the given differential equation.
Then write the general solution.
y +y=csc t
4. For the given differential equation note that t2is a solution. Use the reduction of order
method as explained in the handout to find the general solution.
t2y +ty−4y=0