The order and degree of the differential equation k (d y)/(d x)=∫[1+((d y)/(d x))^2]^ (2)/(3) d x are respectively

Correct answer: B. 2 and 3 Given differential equation is k · (d y)/(d x)=∫[1+((d y)/(d x))^2]^ 2 / 3 · d x On differentiating both sides, we get aligned & k · (d^2 y)/(d x^2)=[1+((d y)/(d x))^2]^ 2 / 3 & (k · (d^2 y)/(d x^2))^3=[1+((d y)/(d x))^2]^2 aligned Now, order of the D.E. =2 Degree of the D.E. =3 .

NDA 2020

Exam: NDA
Year: 2020
Subject: Mathematics
Chapter: Differential Equations

NDA 2020 · Mathematics · Differential Equations

The order and degree of the differential equation k (d y)/(d...

The order and degree of the differential equation

k \frac{d y}{d x}=\int\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{2}{3}} d x

are respectively

Options

A1 and 1
B2 and 3
C2 and 4
D1 and 4

Correct answer

B. 2 and 3

Step-by-step solution

Given differential equation is

k \cdot \frac{d y}{d x}=\int\left[1+\left(\frac{d y}{d x}\right)^2\right]^{2 / 3} \cdot d x

On differentiating both sides, we get

\begin{aligned} & k \cdot \frac{d^2 y}{d x^2}=\left[1+\left(\frac{d y}{d x}\right)^2\right]^{2 / 3} \\ & \Rightarrow\left(k \cdot \frac{d^2 y}{d x^2}\right)^3=\left[1+\left(\frac{d y}{d x}\right)^2\right]^2\end{aligned}

Now, order of the D.E.

=2

Degree of the D.E.

=3

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