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Show that the given differential equati...

Show that the given differential equation is homogeneous and solve each of them.
`x^2(dy)/(dx)=x^2-2y^2+x y`

Text Solution

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Given differential equation is
`x^2(dy)/(dx)=x^2-2y^2+x y`
`(dy)/(dx)` = `(x^2)/ (x^2) - 2 (y^2)/(x^2) + (xy)/(x^2)`
` (dy)/(dx)`= `1 - 2(y/x)^2 + y/x......(i)`
which is homogeneous equation in the form of `f(y/x)`
put `y/x=t` => `y=xt`
diff. w.r.t. x
...
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