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(A) The given differential equation is $x y \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}=0$.$1$. The order of a differe

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Order: $2$,Degree: $1$

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(A) The given differential equation is $x y \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}=0$.$1$. The order of a differential equation is the order of the highest derivative present in the equation. Here,the highest derivative is $\frac{d^{2} y}{d x^{2}}$,so the order is $2$.$2$. The degree of a differential equation is the power of the highest order derivative,provided the equation is a polynomial in derivatives. Here,the highest order derivative $\frac{d^{2} y}{d x^{2}}$ has an exponent of $1$. Since the equation is a polynomial in terms of its derivatives,the degree is $1$.Therefore,the order is $2$ and the degree is $1$.

Find the order and degree,if defined,of the following differential equation:
$x y \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}=0$

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Find the order and degree,if defined,of the following differential equation:$x y \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}=0$