# Differential equation. how to solve?

Submitted by Nelvie Cambay M... on February 5, 2017 - 11:56pm

1. (x^2 + 2xy - 4y^2) dx - ( x^2 - 8xy - 4 y^2)dy=0

2. y(9x-2y)dx-x(6x-y)dy=0; when: x=1; y=1/2

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Submitted by Nelvie Cambay M... on February 5, 2017 - 11:56pm

1. (x^2 + 2xy - 4y^2) dx - ( x^2 - 8xy - 4 y^2)dy=0

2. y(9x-2y)dx-x(6x-y)dy=0; when: x=1; y=1/2

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- 3067 reads

## both equation are homogeneous

both equation are homogeneous. You can use either of the following substitution:

dy = v dx + x dv

dx = v dy + y dv

The result would be separable equation which you can easily solve. And don't forget to revert back to original variables of x and y then apply boundary conditions as necessary.

## thank you po. ☺

thank you po. ☺

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