Slide 1
Undetermined Coefficients
Superposition Approach
Differential Equations
Section 4.4
Slide 2
When does this approach work?

The coefficients on the left-hand side of the
differential equation must be constants.

g(x) must be either a constant, a polynomial
function, an exponential function eax, a sine
or cosine function sin βx or cos βx, or finite
sums and products of these functions.
Slide 3
Method of Solution

Step 1
–

Step 2
–
–

Solve the associated homogeneous equation to obtain the
complementary function yc.
"Guess" at a particular solution of the homogeneous
equation and equate coefficients to obtain the particular
solution yp.
Refer to Table 4.1 on p.172 if necessary until you get the
hang of "guessing".
Step 3
–
Write the general solution y = yc + yp .
Slide 4
What's the catch?

If any terms in yp are duplicates of terms in
yc, then you must multiply by xn, where n is
the smallest positive integer that eliminates
that duplication.