Hi, could someone give me a few tips to start these problems correctly? Thanks!
Let a be a real constant. Consider the equation y''+8y'+ay=0 with boundary conditions y(0)=0 and y(8)=0. For certain discrete values of a, this equation can have non-zero solutions. Find the three smallest values of a for which this is the case.
Suppose that the second order linear equation x^2y''+(x-2x^3)y'-5y=0 has a fundamental set of solutions such that y1(1)=-1, y1'(1)=-3, y2(1)=-4, y2'(1)=-4. Find the Wronskian when x >0.