Which one of the following is a homogeneous d | vedclass

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(C) differential equation of the form $\frac{dy}{dx} = F(x, y)$ is homogeneous if $F(x, y)$ is a homogeneous function of degree $0$. Equivalently,for

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) differential equation of the form $\frac{dy}{dx} = F(x, y)$ is homogeneous if $F(x, y)$ is a homogeneous function of degree $0$. Equivalently,for an equation $M(x, y)dx + N(x, y)dy = 0$,it is homogeneous if both $M(x, y)$ and $N(x, y)$ are homogeneous functions of the same degree.In option $C$,we have $(x^2 + y^2)dx = 2xy dy$.Here,$M(x, y) = x^2 + y^2$,which is a homogeneous function of degree $2$.And $N(x, y) = 2xy$,which is also a homogeneous function of degree $2$.Since both $M$ and $N$ are homogeneous functions of the same degree,the differential equation is homogeneous.

Which one of the following is a homogeneous differential equation?

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