Can someone check my answers?

Hey people,

I would just like a few of my answers to be checked, if anyone wants to,

1) y'=e(-y)-1

I got ln(1-e(y))+x=c, but i think this is wrong(it doesn't match the given answer)

My working was:

dy/dx=1/e(y)-1

dy/dx=(1-e(y))/e(y)

int (1-e(y))/e(y) dy -int 1 dx=0

ln(1-e(y))+x=c

2) (dy/dx)tanx+tany=0

I got sinysinx=c

3) Find the general solution of:

d2y/dx2-5dy/dx+4y=2e(3x)

I got: Ae(4x)+Be(x)-e(3x)

4) d2y/dt2+4y=12cos(2t)

i) find Yc:

I got Yc=Acos(2t)+Bsin(2t)

ii) find the full general solution:

I got y=Acos(2t)+Bsin(2t)+3tsin(2t)

iii) given y'(0)=0 and y(0)=0 find the full solution

I got y=3tsin(2t)

5) evaluate int e(2x)sinx dx via trap rule, simpsons 1/3rd and gauss integration. With 4 strips for trapezoidal/simpsons.

I got:

Trap: 23.02829

Simp: 22.70988612

Gauss: 22.768

Any answer checks would be greatly appreciated, especially for the first question.