1. I need to reduce [tex](a_{1}x + b_{1}y + c_{1})dx + (a_{2}x + b_{2}x +c_{2})dy = 0[/tex] to:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{dy}{dx} = F ( ax + by) [/tex]

with [tex] a_{1}b_{2} = a_{2}b_{1}[/tex]

i.e.:

[tex] a_{1}b_{2}=a_{2}b_{1}[/tex]

[tex]\frac{a_{2}}{a_{1}} = k[/tex] and [tex]\frac{b_{2}}{b_{1}} = k[/tex]

2.

First Try: I solved for dy/dx and tired to deal with the a's and b's. But I am still left with c1 and c2.

Second Try: I tried a different approach by letting x=m+h and y=n+k, then substitute it in and try to solve for h and k. But since the coefficient of dy has 2 x's instead of a x and y, i got a system of 2 "ugly" equations that lead nowhere... (or does it?)

I tried to used the 2 methods in different ways but it seems like I am running in circle.. Can anyone pls help??

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# Homework Help: Help on differential equations PLEASE

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