notes 3-4

# notes 3-4 - y 00-6 y 9 y = 0 When a constant coeﬃcient...

This preview shows pages 1–3. Sign up to view the full content.

SECTION 3.4 REPEATED ROOTS AND REDUCTION OF ORDER EXAMPLE. Solve y 00 - 6 y 0 + 9 y = 0. We need another solution to form a fundamental set. A constant times the known solution won’t work. Let’s try v ( t ) y 1 ( t ). For future use, let’s suppose that y 1 ( t ) is a nonzero solution of y 00 + p ( t ) y 0 + q ( t ) y = 0. We’ll use our guess to try to ﬁnd a y 2 ( t ).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
It’s better not to try to remember formulas, just remember this reduction of order technique for ﬁnding a second solution when we already know one. EXAMPLE, CONTINUED. Find a second solution of
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y 00-6 y + 9 y = 0. When a constant coeﬃcient diﬀerential equation leads to a repeated root, then multiply the exponential solution by t to get a second solution. EXAMPLE. Find the solution of 16 y 00 + 24 y + 9 y = 0 that satisﬁes the initial conditions y (0) = 1, y (0) = 3 / 4. EXAMPLE. Find a fundamental set of solutions of ( x-1) y 00-xy + y = 0 on the interval x > 1, given that y 1 ( x ) = e x is a solution. HOMEWORK: SECTION 3.4...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

notes 3-4 - y 00-6 y 9 y = 0 When a constant coeﬃcient...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online