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(A) The given differential equation is:$\frac{d^{2} y}{d x^{2}}+5 x\left(\frac{d y}{d x}\right)^{2}-6 y=\log x$$1$. The order of a differential equati

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$2, 1$

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(A) The given differential equation is:$\frac{d^{2} y}{d x^{2}}+5 x\left(\frac{d y}{d x}\right)^{2}-6 y=\log x$$1$. The order of a differential equation is the order of the highest derivative present in the equation. Here,the highest derivative is $\frac{d^{2} y}{d x^{2}}$,which is of order $2$. Therefore,the order is $2$.$2$. The degree of a differential equation is the power of the highest order derivative when the equation is expressed as a polynomial in derivatives. The highest order derivative is $\frac{d^{2} y}{d x^{2}}$,and its exponent is $1$. Therefore,the degree is $1$.Thus,the order is $2$ and the degree is $1$.

For the differential equation given below,determine its order and degree (if defined):
$\frac{d^{2} y}{d x^{2}}+5 x\left(\frac{d y}{d x}\right)^{2}-6 y=\log x$

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For the differential equation given below,determine its order and degree (if defined):$\frac{d^{2} y}{d x^{2}}+5 x\left(\frac{d y}{d x}\right)^{2}-6 y=\log x$