If m and n are the order and degree of the differential equation \( 9\displaystyle\frac{d^3y}{dx^3}=\left\{1+\left(\displaystyle\frac{dy}{dx}\right)^2\right\}^{5/2} \) , then the value of 2m+3n is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 12
The highest derivative is \( \frac{d^3y}{dx^3} \), so the order is m = 3. The degree is read only after the fractional power is removed. Squaring both sides:
\( \displaystyle 81\left(\frac{d^3y}{dx^3}\right)^2=\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^5 \)
The highest derivative now appears to the power 2, so n = 2.
\( 2m+3n=6+6=12 \)