p and q are positive integers and n

Question

(D) The given differential equation is $\left(\frac{d^m y}{d x^m} + \frac{d^n y}{d x^n}\right)^{p/q} = 5 \frac{d^r y}{d x^r}$.To find the degree,we ra

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$m=4, p=3$

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(D) The given differential equation is $\left(\frac{d^m y}{d x^m} + \frac{d^n y}{d x^n}\right)^{p/q} = 5 \frac{d^r y}{d x^r}$.To find the degree,we raise both sides to the power $q$ to eliminate the fraction: $\left(\frac{d^m y}{d x^m} + \frac{d^n y}{d x^n}\right)^p = 5^q \left(\frac{d^r y}{d x^r}\right)^q$.The order of a differential equation is the order of the highest derivative present. Given $n Since the order is given as $4$,we have $m = 4$.The degree is the power of the highest order derivative when the equation is expressed as a polynomial in derivatives. Here,the highest order derivative is $\frac{d^m y}{d x^m}$ and its power is $p$.Given the degree is $3$,we have $p = 3$.Thus,$m = 4$ and $p = 3$.

$p$ and $q$ are positive integers and $n < r < m$. If the order and degree of the differential equation $\left(\frac{d^m y}{d x^m} + \frac{d^n y}{d x^n}\right)^{p/q} = 5 \frac{d^r y}{d x^r}$ are respectively $4$ and $3$,then:

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