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1. ### Integration using integrating factor

i know that the left side is ye^-2x but i dont know how to integrate (4x + 10)e^{-2x}
2. ### Integration using integrating factor

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.
3. ### Counter examples to disprove mappings?

yeah. i have got it now! what about c) ? f(x)=2 ??
4. ### Counter examples to disprove mappings?

Thanks! Can You give me some clues for b) ?
5. ### Counter examples to disprove mappings?

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)
6. ### Give example of matrices such that AB=AC but B=/=C

so they could be B = 0 0 and C = 0 0 ?? ............................ 0 1.............1 0
7. ### Give example of matrices such that AB=AC but B=/=C

what does AB = 0 mean? does it mean det(A) x det(B) or matrix A x matrix B?
8. ### Give example of matrices such that AB=AC but 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.
9. ### Give example of matrices such that AB=AC but B=/=C

[b]1. Let M(2,R) be the set of all 2 x 2 matrics over R. Give an example of matrices A,B,C in M(2,R) such that AB=AC, but B is not equal to C. [b]3.
10. ### Groups and subgroups

Inverse element?
11. ### Groups and subgroups

[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...