Q115 / 180 · KCET 2007 · Mathematics

The order and degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^{5}\right]^{\frac{1}{3}}=\frac{d^{2} y}{d x^{2}}$ are respectively

  • A
    1,5
  • B
    2,1
  • C
    2,5
  • Correct answer
    D
    2,3

Solution

Given differential equation is $$ \left[1+\left(\frac{d y}{d x}\right)^{5}\right]^{1 / 3}=\frac{d^{2} y}{d x^{2}} $$ On cubing both sides, we get $$ 1+\left(\frac{d y}{d x}\right)^{5}=\left(\frac{d^{2} y}{d x^{2}}\right)^{3} $$ Now, order is 2 and degree is 3 .

Hence, the correct answer is option: 'D'.

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