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NDA 2023 Maths · Mathematics · Differential Equations · medium

The curvature-type equation [1+(dy/dx)^2]^3/2=(d^2y)/(dx^2 is first cleared of its fractional power. After this, its order and degree are respectively

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The curvature-type equation [1+(dydx)2]3/2=d2ydx2\left[1+\left(\dfrac{dy}{dx}\right)^2\right]^{3/2}=\dfrac{d^2y}{dx^2} is first cleared of its fractional power. After this, its order and degree are respectively
  1. A. 22 and 32\dfrac32
  2. B. 22 and 11
  3. C. 22 and 22
  4. D. 33 and 22
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Answer: (C) 22 and 22

The degree is defined after clearing fractional powers. Squaring both sides gives [1+(y′)2]3=(y′′)2\left[1+(y')^2\right]^3=(y'')^2, a polynomial in the derivatives where the highest derivative y′′y'' has power 22. Hence the order is 22 and the degree is 22, not 32\dfrac32.
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