Homework Statement
Integrate dy/dx=2y+4x+10
The Attempt at a Solution
dy/dx-2y=4x+10
Integrating factor = e^(-2)dx=e^-2x
multiply both sides by IF. (e^-2x)dy/dx-2y(e^-2x)=(e^-2x)(4x+10)
dy/dx(e^-2x y)=(e^-2x)(4x+10)
i dont know what to do next.
give counter examples to disprove the following statements:
a) a real valued odd function cannot be strictly monotonic
b) a real valued periodic function must be odd or even
c) a real valued monotonic function cannot be even
a) sinh(x) ??
b)
c)
(A^-1)AB=(A^-1)AC so B=C. This shows that A must have no inverse element. So A could be
1 0
0 0
because det(a)=1-0=0 so A has no inverse. I dont know what A and B could be.
[b]1. Let G be a group containing subgroups H and K such that we can find an element h e H-K an an element k e K - H. Prove that h o k is not a subgroup of H U K. Deduce that H U K is not a subgroup of G.
I have proved that h o k is not in H U K but I dont know how to deduce that H U K is not...