Question

If m and n are the order and degree of the differential equation $\left( \frac{d^{2}y}{dx^{2}} \right)^{5}$+ 4$\frac{\begin{pmatrix} d^{2}y \\ dx^{2} \end{pmatrix}^{3}}{\begin{pmatrix} d^{3}y \\ dx^{3} \end{pmatrix}}$ + $\frac{d^{3}y}{dx^{3}}$ = x² – 1 then :

• A. m = 3, n = 5
• B. m = 3, n = 1
• C. m = 3, n = 3
• D. m = 3, n = 2

Answer 1

Answer: (D)

m = 3, n = 2

Answer 2

$\left( \frac{d^{2}y}{dx^{2}} \right)^{5}$+ 4$\left( \frac{d^{2}y}{dx^{2}} \right)^{3}$+ $\left( \frac{d^{3}y}{dx^{3}} \right)^{2}$

= (x²–1) $\frac{d^{3}y}{dx^{3}}$

order = 3 = m

Degree = 2 = n