If m and n are respectively the order and degree of the differential equation :
$\left(\frac{d^2 y}{d x^2}\right)^5+6 \frac{\left(\frac{d^2 y}{d x^2}\right)^3}{\frac{d^3 y}{d x^3}}+\frac{d^3 y}{d x^3}=x^2+5$, then :
Answer & explanation
Correct answer: option 3
$\left(\frac{d^2 y}{d x^2}\right)^5+6 \frac{\left(\frac{d^2 y}{d x^2}\right)^3}{\frac{d^3 y}{d x^3}}+\frac{d^3 y}{d x^3}=x^2+5$
Multiplying eq by $\frac{d^3y}{dx^3}$ (as power of all terms need to be ≥ 0)
so $\left(\frac{d^3 y}{d x^3}\right)\left(\frac{d^2 y}{d x^2}\right)^5+6\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d^3 y}{d x^3}\right)^2=\left(x^2+5\right) \frac{d^3 y}{d x^2}$
so order = highest order of derivative = 3
degree = highest power of term of order derivative = 2