Practicing Success
If m is the degree and n is the order of the given differential equation \(\frac{x^3\left(\frac{d^3 y}{d x^3}\right)^2+2 x^2\left(\frac{d^2 y}{d x^2}\right)^3}{(x+1)^5}=\left(3 x-\frac{d^2 y}{d x^2}\right)^4 \) |
m – n = 2 m + n = 5 m = 4, n = 3 Order (n) is 3 but degree (m) is not defined |
m + n = 5 |
\(\frac{x^3\left(\frac{d^3 y}{d x^3}\right)^2+2 x^2\left(\frac{d^2 y}{d x^2}\right)^3}{(x+1)^5}=\left(3 x-\frac{d^2 y}{d x^2}\right)^4 \) $⇒x^3(\frac{d^3 y}{d x^3})^2+2x^2(\frac{d^2 y}{d x^2})^3-(x+1)^5(3x-\frac{d^2 y}{d x^2})^4=0$ ∴ order (n) = 3 Degree (m) = 2 ∴ m + n = 5 option 2 is correct. |