If m and n are the order and degree of the differential equation ( d 2 y d x 2 ) 5 + 4 ( d 2 y d x 2 ) 3 ( d 3 y d x 3 ) + d 3 y d x 3 = x 2 - 1 , then:

Question

If $m$ and $n$ are the order and degree of the differential equation ${(\frac{d^{2} y}{d x^{2}})}^{5} + 4 \frac{{(\frac{d^{2} y}{d x^{2}})}^{3}}{(\frac{d^{3} y}{d x^{3}})} + \frac{d^{3} y}{d x^{3}} = x^{2} - 1$ , then:

Smart Achievers · Accepted Answer

(4)

Ans. $m = 3$ and $n = 2$

Explanation:

The highest order $(m)$ of the given equation is $\frac{d^{3} y}{d x^{3}} = 3$

and degree $(n)$ of the given equation is ${(\frac{d^{3} y}{d x^{3}})}^{2} = 2 .$

Therefore, $m = 3$ and $n = 2$ .

Solution

Q.
If $m$ and $n$ are the order and degree of the differential equation ${(\frac{d^{2} y}{d x^{2}})}^{5} + 4 \frac{{(\frac{d^{2} y}{d x^{2}})}^{3}}{(\frac{d^{3} y}{d x^{3}})} + \frac{d^{3} y}{d x^{3}} = x^{2} - 1$ , then:

1 $m = 3$ and $n = 5$

2 $m = 3$ and $n = 1$

3 $m = 3$ and $n = 3$

4 $m = 3$ and $n = 2$

Ans.
(4)

Ans. $m = 3$ and $n = 2$

Explanation:

The highest order $(m)$ of the given equation is $\frac{d^{3} y}{d x^{3}} = 3$

and degree $(n)$ of the given equation is ${(\frac{d^{3} y}{d x^{3}})}^{2} = 2 .$

Therefore, $m = 3$ and $n = 2$ .

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Solution

Q. If m and n are the order and degree of the differential equation (d2ydx2)5+4(d2ydx2)3(d3ydx3)+d3ydx3=x2-1, then:

1 m=3 and n=5

2 m=3 and n=1

3 m=3 and n=3

4 m=3 and n=2

Ans. (4) Ans. m=3 and n=2 Explanation: The highest order (m) of the given equation is d3ydx3=3 and degree (n) of the given equation is (d3ydx3)2=2. Therefore, m=3 and n=2.