{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MATH24 Lecture 3

# MATH24 Lecture 3 - MATH24 Differential Equations Equations...

This preview shows pages 1–6. Sign up to view the full content.

MATH24 Differential Equations

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

View Full Document
Equations with Homogeneous Coefficients The differential equation M(x, y)dx + N(x, y)dy is homogeneous if both M and N are homogeneous and are of the same degree. Theorem: 1. If M(x, y) and N(x, y) are both homogeneous and of the same degree, the function or N/M is of degree 0. 2. If f(x, y) is homogeneous of degree zero in x + y, then f(x, y) is a function of y/x alone.
General Solution of A Homogeneous D. E. If M(x, y) and N(x, y) are homogeneous and of degree zero, then the ratio M/N of N/M can be expressed as a function of single variable alone, say v. Thus, the substitution x = vy or y = vx will transform the equation to a variable separable D. E. Note: A differential equation is homogeneous if all the terms are of the same degree.

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

View Full Document
Examples Test for homogeneity. 1. (x 2 + y 2 )dx + xydy = 0 M = x 2 + y 2 , homogeneous of degree 2 N = xy, homogeneous of degree 2 Thereforem, the D. E. is homogeneous. 2. (3x + 2y)dx – (x 2 + 2xy + y 2 )dy = 0 M = 3x + 2y, homogeneous of degree 1 N = x 2 + 2xy + y 2 , homogeneous of degree 2.
Examples Test whether each equation is homogeneous or not. If it is

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 16

MATH24 Lecture 3 - MATH24 Differential Equations Equations...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online