NDA 2018 Maths · Mathematics · Differential Equations · easy

The order and degree of the differential equation y=xdy/dx+√(1+(dy/dx)^2 are respectively

Single correct option

The order and degree of the differential equation

y=x\frac{dy}{dx}+\sqrt{1+\left(\frac{dy}{dx}\right)^2}

are respectively

A. $1$ and $1$
B. $1$ and $2$
C. $2$ and $1$
D. $1$ and $\frac12$

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Answer: (B) $1$ and $2$

Isolate the radical and square:

\left(y-x\frac{dy}{dx}\right)^2=1+\left(\frac{dy}{dx}\right)^2

. The highest derivative is the first, appearing to the power 2 once the radical is removed, so the order is 1 and the degree is 2. The fractional power

\frac12

is not a valid degree.

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