- #1
unseensoul
- 47
- 0
Why can't there be common terms on both complementary function and particular integral when solving differential equations?
For instance,
dy/dx + 3y = exp(-x) + exp(-3x)
y(CF) = Aexp(−3x)
y(PI) = Cexp(−x) + Dxexp(−3x)
The term Dexp(-3x) in the P.I. has to be multiplied by x to be linearly independent of Aexp(-3x) in the C.F.. Why? What would happen if it wasn't?
For instance,
dy/dx + 3y = exp(-x) + exp(-3x)
y(CF) = Aexp(−3x)
y(PI) = Cexp(−x) + Dxexp(−3x)
The term Dexp(-3x) in the P.I. has to be multiplied by x to be linearly independent of Aexp(-3x) in the C.F.. Why? What would happen if it wasn't?