a)
Select all solutions of (d^2/dx^2)y(x)+64y(x)=0.
y(x)=3cos(8x)
y(x)=3cos(4x)
y(x)=C1sin(8x)+C2cos(8x)
y(x)=−4sin(8x)
y(x)=C2cos(8x)
b)
Select all solutions of (d^2/dx^2)y(x)+36y(x)=0.
y(x)=C2cos(3x)
y(x)=C1sin(3x)
y(x)=3cos(3x)
y(x)=3cos(6x)
y(x)=3sin(3x)+8cos(3x)
solve by determinants
a.x+y+z=0
3x-y+2z=-1
2x+3y+3z=-5
b. x+2z=1
2x-3y=3
y+z=1
c. x+y+z=10
3x-y=0
3y-2z=-3
d. -8x+5z=-19
-7x+5y=4
-2y+3z=3
e. -x+2y+z-5=0
3x-y-z+7=0
-2x+4y+2z-10=0
f. 1/x+1/y+1/z=12
4/x-3/y=0
2/y-1/z=3