8. Without solving the following differential equations verify if the set of solutions is a vector space a) f"(x) = x; b) x² f"(x) – 2f(x) = 0; c) f'(x) = 2/F(x). Hint: verify if the set of solutions is a vector subspace of the space of all functions

Q: 1) Let f(z,y)- . Compute DS(z,y) where u- (4-9)

A:

Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

A:

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

A:

Q: Verify that the vector X, is a particular solution of the given nonhomogeneous linear system. 2 1 X'…

A:

Q: of the form y₁ = (1+₁2+ a₂x² + 3x³ + ...) 32 = x2(1+b₁x + b₂x² + b₂x³ + ...) where T₁ > T2- Enter…

A:

Q: 5. Let u= w= [-]-[], and w (a) Show that w is not a linear combination of u. (b) Show that u and V…

A: We have to show that-w is not a linear combination of u,u and v are linearly independent,w is a…

Q: f(2) 1 dt, then f'(z) = ++1

A:

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

A:

Q: Exercise 6: Suppose f and g are functions such that: -3 f = 1, i=7, f = 5, -3 Г» g = 6, g = 3, :-4.…

A: Suppose f and g are functions such that

Q: 8(x) 48. f(x) 2 - x' In Exercises 51–60, show that f(g(x)) = x an dom x - 1 g(x) of 51,fx) = 2r + 1,…

A:

Q: Determine each of the following derivative values that involve functions that are defined in terms…

A:

Q: 9. Explain why dt r1/I dt 1+t2 1+t? is valid for any x > 0.

A: