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What is the degree of the differential equation \(\rm \left(\frac {d^3y}{dx^3}\right)^{1/2} = \left(\frac {d^2y}{dx^2}\right)^{2}\) ?
1. 2
2. 3
3. 5
4. 1

1 Answer

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Best answer
Correct Answer - Option 4 : 1

Concept:

Degree: The degree of a differential equation is the power of the highest derivative.

Calculation:

We have, \(\rm \left(\frac {d^3y}{dx^3}\right)^{1/2} = \left(\frac {d^2y}{dx^2}\right)^{2}\)

Squaring both the sides, we get

\(\rm \left(\frac {d^3y}{dx^3}\right) = \left(\frac {d^2y}{dx^2}\right)^{4}\)

Here highest derivative is \(\rm \left(\frac {d^3y}{dx^3}\right)\)

∴Degree = power of \(\rm \left(\frac {d^3y}{dx^3}\right)\)= 1

Hence, option (4) is correct. 

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