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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Differential Equations

NDA 2024 · Mathematics · Differential Equations

What are the order and degree respectively of the differential...

What are the order and degree respectively of the differential equation \left\{2-\left(\frac{d y}{d x}\right)^2\right\}^{0.6}=\frac{d^2 y}{d x^2} ?

Options

  1. A2,2
  2. B2,3
  3. C5,2
  4. D2,5

Correct answer

D. 2,5

Step-by-step solution

{2−(dydx)2}0.6=d2ydx2\left\{2-\left(\frac{d y}{d x}\right)^2\right\}^{0.6}=\frac{d^2 y}{d x^2} Removing decimal power/fraction power both sides {2−(dydx)2}3/5=(d2ydx2)5\left\{2-\left(\frac{d y}{d x}\right)^2\right\}^{3 / 5}=\left(\frac{d^2 y}{d x^2}\right)^5 Raise power of 5 both sides {2−(dydx)2}35×5=(d2ydx2)5⇒{2−(dydx)2}3=(d2ydx2)5\begin{aligned} & \left\{2-\left(\frac{d y}{d x}\right)^2\right\}^{\frac{3}{5} \times 5}=\left(\frac{d^2 y}{d x^2}\right)^5 \\ \Rightarrow \quad & \left\{2-\left(\frac{d y}{d x}\right)^2\right\}^3=\left(\frac{d^2 y}{d x^2}\right)^5 \end{aligned} Hence,  Order =2 Power =5\begin{aligned} \text{ Order } & =2 \\ \text{ Power } & =5 \end{aligned}
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