Question

The sum of the degree and order of the differential equation \[\sqrt{\frac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}}=\sqrt[5]{\frac{\mathrm{d}y}{\mathrm{d}x}-5}\] is

Options

• 1

• 3

• 5

• 7

Answer 1

7

Explanation:

\[\sqrt{\frac{\mathrm{d}^2y}{\mathrm{d}x^2}}=\sqrt[5]{\frac{\mathrm{d}y}{\mathrm{d}x}-5}\]

Taking the tenth power of both sides, we get

\[\left(\frac{\mathrm{d}^2y}{\mathrm{d}x^2}\right)^5=\left(\frac{\mathrm{d}y}{\mathrm{d}x}-5\right)^2\]

∴ By definition,

order = 2 and degree = 5

∴ Order + degree = 2 + 5 = 7