Originally Posted by
deragon999 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.