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JEE Main 2017 · Mathematics · Differential Equations · medium

The order and degree of the differential equation [1+(dy/dx)^2]^3/2=(d^2y)/(dx^2 are respectively

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The order and degree of the differential equation [1+(dydx)2]3/2=d2ydx2\left[1+\left(\dfrac{dy}{dx}\right)^2\right]^{3/2}=\dfrac{d^2y}{dx^2} are respectively
  1. A. 2, 322,\ \dfrac32
  2. B. 2, 32,\ 3
  3. C. 2, 22,\ 2
  4. D. 1, 21,\ 2
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Answer: (C) 2, 22,\ 2

The highest derivative is y′′y'', so the order is 2. To find the degree remove the fractional power by squaring: [1+(y′)2]3=(y′′)2\left[1+(y')^2\right]^3=(y'')^2. Now the equation is polynomial in the derivatives and the power of the highest-order derivative y′′y'' is 2. So the degree is 2 (not 3/23/2 and not 3).
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