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[" Question 1."(x^(2)+xy)dy=(x^(2)+y^(2)...

[" Question 1."(x^(2)+xy)dy=(x^(2)+y^(2))dx],[" (i) First check the homogeneous nature of the equatio- "]

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(dy)/(dx)=(x^(2)-y^(2))/(xy)

x^(2)(dy)/(dx)+y^(2)=xy

x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy

x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy

x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy

(dy)/(dx) = (x^(2)+y^(2))/(xy)

(1-xy+x^(2)y^(2))dx=x^(2)dy

Show that the differential equation (x^(2)+xy)dy=(x^(2)+y^(2))dx is homogenous and solve it.