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# Solve the differential equation$y\;e^{\large\frac{x}{y}}\;dx=\bigg(x\;e^{\Large\frac{x}{y}}+y^2\bigg)dy\;(y\neq0)$

• If the linear differential equation is of the form $\large\frac{dx}{dy}$$= F(x,y), is said to be homogenous if F(x,y) is a homogenous function of degree 0. • This type of equation can be solved by substituting x= vy and \large\frac{dx}{dy} =$$ v+y\large\frac{dv}{dy}$
Given :$y\;e^{\large\frac{x}{y}}\;dx=\bigg(x\;e^\frac{x}{y}+y^2\bigg)dy$
we can write the equation as $\large\frac{dx}{dy} = \frac{[xe^{\Large(x/y)} +y^2]}{y.e^{\Large(x/y)} }$