If p and q are order and degree of differential equation y-2 -d-2 y-dx-2-2 - 3x -dy-dx-1-3 - x-2 y-2 - sin x- thenp gt- qp-q - 1-2p - qp lt- q

The correct option is D p lt; qy^2 (d^2 y/dx^2)^2 + x62 y^2 sin x = 3x (dy/dx)^1/3 (y^2 (d^2 y/dx^2)^2 + x^2 y^2)^3 = 9x^3 (dy/dx) Degree = 6 = q ∴ p ...

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Standard XII

Mathematics

Degree of a Differential Equations

If p and q ar...

Question

If p and q are order and degree of differential equation $y^{2} (\frac{d^{2} y}{d x^{2}})^{2} + 3 x (\frac{d y}{d x})^{\frac{1}{3}} + x^{2} y^{2} = s i n x$ , then

p > q

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\frac{p}{q} = \frac{1}{2}

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p = q

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p < q

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Solution

The correct option is D $p < q$
$y^{2} (\frac{d^{2} y}{d x^{2}})^{2} + x 62 y^{2} - s i n x = - 3 x (\frac{d y}{d x})^{\frac{1}{3}} (y^{2} (\frac{d^{2} y}{d x^{2}})^{2} + x^{2} y^{2})^{3} = - 9 x^{3} (\frac{d y}{d x})$
Degree = 6 = q
$∴ p = 2 < q$

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Q. If p and q are order and degree of differential equation

y^{2} (\frac{d^{2} y}{d x^{2}})^{2} + 3 x (\frac{d y}{d x})^{\frac{1}{3}} + x^{2} y^{2} = s i n x

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If p and q are order and degree of differential equation y2(d2ydx2)2+3x(dydx)13+x2y2=sinx, then

The correct option is D p<qy2(d2ydx2)2+x62y2−sinx=−3x(dydx)13(y2(d2ydx2)2+x2y2)3=−9x3(dydx) Degree = 6 = q ∴p=2<q

If p and q are order and degree of differential equation $y^{2} (\frac{d^{2} y}{d x^{2}})^{2} + 3 x (\frac{d y}{d x})^{\frac{1}{3}} + x^{2} y^{2} = s i n x$ , then

The correct option is D $p < q$
$y^{2} (\frac{d^{2} y}{d x^{2}})^{2} + x 62 y^{2} - s i n x = - 3 x (\frac{d y}{d x})^{\frac{1}{3}} (y^{2} (\frac{d^{2} y}{d x^{2}})^{2} + x^{2} y^{2})^{3} = - 9 x^{3} (\frac{d y}{d x})$
Degree = 6 = q
$∴ p = 2 < q$