- #1
james.farrow
- 44
- 0
I have the following equation
d^2y/dx^2 +4dy/dx +8y = 4sin(2x) - 12cos(2x) y(0)=1 & y'(0)=-6
For the auxillary equation I have (m + 2)^2 = sqrt -4
which gives m=-2-2i & m=-2+2i
Which gives y=e^-2x(Ccos(-2x) + Dsin(-2x))
Now to tackle particular integral.
Try y=acos(2x) + bsin(2x)
After differentiatiing twice and equating I have a=-5 and b=-9
Finally I get y=e^-2x(Ccos(-2x) + Dsin(-2x)) - 5cos(2x) -9sin(2x)
After aplying the initial conditions my final answer is
y=6e^-2xcos(-2x) - 18e^-2sin(-2x) - 5cos(2x) - 9sin(2x)
In all my working it is only e that is raised to the power of -2x, I know it looks like the whole statement is raised but it isnt, the e^-2x is multiplied by the trig expression.
James
d^2y/dx^2 +4dy/dx +8y = 4sin(2x) - 12cos(2x) y(0)=1 & y'(0)=-6
For the auxillary equation I have (m + 2)^2 = sqrt -4
which gives m=-2-2i & m=-2+2i
Which gives y=e^-2x(Ccos(-2x) + Dsin(-2x))
Now to tackle particular integral.
Try y=acos(2x) + bsin(2x)
After differentiatiing twice and equating I have a=-5 and b=-9
Finally I get y=e^-2x(Ccos(-2x) + Dsin(-2x)) - 5cos(2x) -9sin(2x)
After aplying the initial conditions my final answer is
y=6e^-2xcos(-2x) - 18e^-2sin(-2x) - 5cos(2x) - 9sin(2x)
In all my working it is only e that is raised to the power of -2x, I know it looks like the whole statement is raised but it isnt, the e^-2x is multiplied by the trig expression.
James