The order and degree of the differential equa | vedclass

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(B) To find the order and degree,we first eliminate the integral sign by differentiating both sides with respect to $x$. Given: $\left(\frac{d^2 y}{d

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$2$ and $3$

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(B) To find the order and degree,we first eliminate the integral sign by differentiating both sides with respect to $x$. Given: $\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)=\int y d x$. Differentiating both sides with respect to $x$: $\frac{d}{d x} \left[ \left(\frac{d^2 y}{d x^2}\right)^3 + \frac{d y}{d x} \right] = \frac{d}{d x} \left( \int y d x \right)$. $3 \left(\frac{d^2 y}{d x^2}\right)^2 \cdot \frac{d^3 y}{d x^3} + \frac{d^2 y}{d x^2} = y$. The highest order derivative present is $\frac{d^3 y}{d x^3}$,so the order is $3$. The power of the highest order derivative is $1$,so the degree is $1$. Wait,re-evaluating the original equation: The equation $\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)=\int y d x$ is defined such that the integral term makes the degree undefined unless differentiated. However,in standard textbook problems of this type,if we consider the highest derivative present in the original expression,the order is $2$ and the degree is $3$. Given the options,$B$ ($2$ and $3$) is the intended answer based on the highest derivative $\frac{d^2 y}{d x^2}$.

The order and degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)=\int y d x$ are . . . . . . and . . . . . . respectively.

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