If m and n are the order and degree of the differential equation (y2)^5 + 4(y2)^3/y3 + y3 = x^2 - 1,

Question

If m and n are the order and degree of the differential equation \((y_2)^5 + \frac{4(y_2)^3}{y_3}+y_3=x^2-1,\) then

A. m = 3, n = 3

B. m = 3, n = 2

C. n = 3, n = 5

D. m = 3, n = 1

Answer 1

Correct answer is B.

(y₂)⁵ + 4(y₂)³/y₃ + y³ = x² - 1

\(\Rightarrow y_3(y_2)^5 + 4(y_2)^3 \) \(+ (y_3)^2 = y_3(x^2 - 1)\)

Order = Highest order derivative present in the differential equation.

∴ Order = 3 = m

Degree = Highest power of highest order derivative which is (y₃)²

∴ Degree = 2 = n

∴ m = 3, n = 2