My Yp expression is:
But for this one,
its:
For the second one, the expression for cos(5x) is written as [tex]
but for the first one, sin(9x) its :
Why does the second instance have an x infront of the cos and sin? Whats the rule here?
My Yp expression is:
But for this one,
its:
For the second one, the expression for cos(5x) is written as [tex]
but for the first one, sin(9x) its :
Why does the second instance have an x infront of the cos and sin? Whats the rule here?
The rule here is that functions that show up in the homogeneous solution (that is, the differential equation LHS = 0), need to be "enhanced" in order not to be annihilated by the LHS's operator when you plug it into the DE. Notice that in your second yp, there's an x multiplying the exponential. That's because in that case, the exponential is already a part of the homogeneous solution. In the first problem, the trig functions are both in the homogeneous solution. Make sense?