![ydx+(y-x)dy=0\\\\\Rightarrow ydx+ydy-xdy=0\\\\\\\Rightarrow \dfrac{ydx+ydy-xdy}{y^2}=\dfrac{0}{y^2}~~~~~~~~~~~~~~~~~~~~[\textup{dividing both sides by }y^2]\\\\\\\Rightarrow \dfrac{ydx-xdy}{y^2}+\dfrac{1}{y}dy=0\\\\\\\Rightarrow d\left(\dfrac{x}{y}\right)+d(\log y)=0.](/tpl/images/0081/8574/50f61.png)
![\int d\left(\dfrac{x}{y}\right)+\int d(\log y)=C~~~~~~~[\textup{where C is the constant of integration}]\\\\\\\Rightarrow \dfrac{x}{y}+\log y=C\\\\\Rightarrow x+y\log y=Cy.](/tpl/images/0081/8574/08e3b.png)
.ydx+(y-x)dy=0
be as thorough as possible when explaining this, i'm struggling very much tryin...
Mathematics, 12.07.2019 18:20 cl6205071
ydx+(y-x)dy=0
be as thorough as possible when explaining this, i'm struggling very much trying to solve ode's
Answers: 2
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