2_3a - Solutions 2.3-Page 131 Problem 1 Find the general...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Solutions 2.3-Page 131 Problem 1 Find the general solutions of the differential equations. 0 4 = y y The first step is to find the roots of the characteristic equation. 2 , 2 0 ) 2 )( 2 ( 0 4 2 = = + = r r r r Since the roots are real and distinct, the general solution is x x e c e c x y 2 2 2 1 ) ( + =
Background image of page 1

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

View Full DocumentRight Arrow Icon
Problem 9 Find the general solutions of the differential equations. 0 25 8 = + + y y y The characteristic equation is . The roots can be found using the quadratic equation formula or a calculator. 0 25 8 2 = + + r r The roots are . i r 3 4 ± = The general solution is based on Theorem 3 on page 128. ) 3 sin 3 cos ( ) ( 2 1 4 x c x c e x y x + =
Background image of page 2
Problem 21 Solve the initial value problems. 4 3 0; (0) 7, (0) 11 yyy y y ′′ −+= = = The characteristic equation is . The roots can be found using the quadratic equation formula or a calculator. 0 3 4 2 = + r r The roots are . 1 , 3 = r The general solution is . The initial conditions are used to find the constants.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

2_3a - Solutions 2.3-Page 131 Problem 1 Find the general...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online