Question

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This question is only for 12th STUDENT..

Answer - (D)

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Answer 1

Solution :

The given differentiatial equation is

$y^{2}\big(\frac{d^{2}y}{dx^{2}}\big)^{2}+3x\big(\frac{dy}{dx}\big)^{1/3}+x^{2}y^{2}=sinx$

The highest ordered derivative involved in the given differentiatial equation is $\frac{d^{2}y}{dx^{2}}$ and thus the order of the equation is 2.

The degree of any differential equation is the power of the highest derivative involved in the equation where the power of the other derivatives present in the equation must be non-negative integers.

But the power of $\frac{dy}{dx}$ is 1/3 which isn't satisfactory. So we take that term completely to one side of the equation and others to another. Then we power up the equation with 3 and thus the power of $\frac{d^{2}y}{dx^{2}}$ becomes 2 × 3 = 6, i.e., the degree of the given differential equation is 6.

By the given condition,

p = 2 and q = 6

Therefore, p < q [ option (D) ]

Answer 2

Answer:

2 × 3 = 6, i.e., the degree of the given differential equation is 6.

By the given condition,

p = 2 and q = 6

Therefore, p < q [ option (D) ]