1. Math
  2. Advanced Math
  3. 1 2 3 lt please solve for this one...

Question: 1 2 3 lt please solve for this one...

Question details

1. Recall that the general homogeneous linear ODE of order n takes the form dy for functions ao()an() with an() 0. Suppose f(x) and g(x) are uppose J(T) and g(T) are solutions to this ODE. Show that: (a) For any constant λ, the function λ/is also a solution to this ODE. (b) The function f +g is also a solution to this ODE. If youve taken a linear algebra course, then you know that this says that the set Sof solutions to the above ODE is a subspace of the vector space of all differentiable functions (defined on an open interval, say, with the usual notions of addition and scalar multiplication)

2. the ODE y-y-Gy-0. Hint: Write f(z) _ f,(z) _ 6/(2) p(m)emz for a quadratic polynomial p. Note that eme > 0 for all T, so p(menz-0 iff p(m) 0. Factor or use the Q.F. to find the roots of p.

3. Use the results of the previous two exercises to find a two-parameter family<--------- please solve for this one

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution