SpecialTransformation

# SpecialTransformation - Special Transformation There are...

This preview shows pages 1–2. Sign up to view the full content.

Special Transformation There are certain equations that can be transformed into a more basic type using a suitable transformation. The equations have the form: (a 1 x + b 1 y + c 1 ) dx + (a 2 x + b 2 y + c 2 ) dy = 0 where a 1 , b 1 , c 1 , a 2 , b 2 , c 2 are constants. There are two different kind of transformations according to relationships among the constants. Case 1 : a 2 a 1 ! b 2 b 1 Solve the system a 1 h + b 1 k + c 1 = 0 a 2 h + b 2 k + c 2 = 0 because of the imposed condition the system has a unique solution (h,k). Then, the transformation: x = X + h y = Y + k will change the original equation into a homogeneous equation in the variable X and Y, (a 1 X + b 1 Y) dX + (a 2 X + b 2 Y) dY = 0 Case 2 : a 2 a 1 = b 1 b 2 = k The transformation z = a 1 x + b 1 y changes the original equation into a separable equation in the variables z and x. Examples : Solve the equations 1) (2x - 5x + 3) dx – (2x + 4y – 6) dy = 0 Since 2/2 4/-5, let’s solve the system 2h - 5k + 3 = 0

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 / 3

SpecialTransformation - Special Transformation There are...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online