# Slide 1 Slide 2 Undetermined Coefficients

```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.
&quot;Guess&quot; 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 &quot;guessing&quot;.
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.
```