The degree and order of the differential equation xy d 3 y - dx 3- x d 2 y - dx 2- y - dy - dx -0 isA- 2 and 3B- 1 and 3C- 3 and 3D- 3 and 1

The correct option is A 2 and 3xy d^3y/dx^3 + xd^2y/dx^2 y √(dy/dx) = 0 ⇒ nbsp; xy d^3y/dx^3 + xd^2y/dx^2 = nbsp;y √(dy/dx) ⇒( xy d^3y/dx^3 + xd^2y/dx^2) ...

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Standard XII

Mathematics

Chain Rule of Differentiation

The degree an...

Question

The degree and order of the differential equation $x y \frac{d^{3} y}{d x^{3}} + x \frac{d^{2} y}{d x^{2}} - y \sqrt{\frac{d y}{d x}} = 0$ is

1

and

3

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2

and

3

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3

and

3

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3

and

1

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Solution

The correct option is B $2$ and $3$
$x y \frac{d^{3} y}{d x^{3}} + x \frac{d^{2} y}{d x^{2}} - y \sqrt{\frac{d y}{d x}} = 0 \Rightarrow x y \frac{d^{3} y}{d x^{3}} + x \frac{d^{2} y}{d x^{2}} = y \sqrt{\frac{d y}{d x}} \Rightarrow {(x y \frac{d^{3} y}{d x^{3}} + x \frac{d^{2} y}{d x^{2}})}^{2} = y \frac{d y}{d x}$
The highest derivative in the D.E is $\frac{d^{3} y}{d x^{3}}$ so the order $= 3$
The power of the highest order derivative in the D.E is $= 2$
Hence the degree $= 2$ and order $= 3$

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The degree and order of the differential equation xyd3ydx3+xd2ydx2−y√dydx=0 is

The correct option is B 2 and 3xyd3ydx3+xd2ydx2−y√dydx=0⇒xyd3ydx3+xd2ydx2=y√dydx⇒(xyd3ydx3+xd2ydx2)2=ydydx The highest derivative in the D.E is d3ydx3 so the order =3 The power of the highest order derivative in the D.E is =2 Hence the degree =2 and order =3

The degree and order of the differential equation $x y \frac{d^{3} y}{d x^{3}} + x \frac{d^{2} y}{d x^{2}} - y \sqrt{\frac{d y}{d x}} = 0$ is