The order and degree of the differential equa | vedclass

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(A) The given differential equation is $\left(y^{\prime \prime \prime}\right)^3+\left(y^{\prime \prime}\right)^4+\left(y^{\prime}\right)^4+y=7$. The o

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$3$ and $3$

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(A) The given differential equation is $\left(y^{\prime \prime \prime}\right)^3+\left(y^{\prime \prime}\right)^4+\left(y^{\prime}\right)^4+y=7$. The order of a differential equation is the order of the highest derivative present in the equation. Here,the highest derivative is $y^{\prime \prime \prime}$,which is of order $3$. Thus,the order of the differential equation is $3$. 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 $y^{\prime \prime \prime}$ and its exponent is $3$. Therefore,the degree of the differential equation is $3$. Hence,the order and degree are $3$ and $3$ respectively.

The order and degree of the differential equation $\left(y^{\prime \prime \prime}\right)^3+\left(y^{\prime \prime}\right)^4+\left(y^{\prime}\right)^4+y=7$ are . . . . . . respectively.

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