If p and q are order and degree of differential equation y 2 d 2 y - dx 22-3 x dy - dx 1-3- x 2 y 2-sin x- thenA- p - q -1-2B- p-qC- pq

The correct option is C p lt; qy^2 (d^2y/dx^2 )^2 +x^2y^2 sin x= 3x (dy/dx )^1/3 (y^2 (d^2y/dx^2 )^2+x^2y^2 sin x )^3 = 9x^3 (dy/dx ) Here order = 2 = p D ...

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Byju's Answer

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
$y^{2} {(\frac{d^{2} y}{d x^{2}})}^{2} + x^{2} y^{2} - s i n x = - 3 x {(\frac{d y}{d x})}^{\frac{1}{3}} {(y^{2} {(\frac{d^{2} y}{d x^{2}})}^{2} + x^{2} y^{2} - s i n x)}^{3} = - 9 x^{3} (\frac{d y}{d x})$
Here order = 2 = p
Degree = 6 = q
$∴ p < q$

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Similar questions

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

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

Q. If

p

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q

are order and degree of differential equation

y^{2} (\frac{d^{2} y}{d x^{2}}) + 3 x {(\frac{d y}{d x})}^{\frac{1}{3}} + x^{2} y^{2} = sin x

then find

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Q. If m, n are the order and degree of

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

is:

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

y \frac{d y}{d x} + x^{3} \frac{d^{2} y}{d x^{2}} + x y

= cos x, then
(a) p < q
(b) p = q
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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+x2y2−sinx=−3x(dydx)13(y2(d2ydx2)2+x2y2−sinx)3=−9x3(dydx) Here order = 2 = p Degree = 6 = q ∴p<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
$y^{2} {(\frac{d^{2} y}{d x^{2}})}^{2} + x^{2} y^{2} - s i n x = - 3 x {(\frac{d y}{d x})}^{\frac{1}{3}} {(y^{2} {(\frac{d^{2} y}{d x^{2}})}^{2} + x^{2} y^{2} - s i n x)}^{3} = - 9 x^{3} (\frac{d y}{d x})$
Here order = 2 = p
Degree = 6 = q
$∴ p < q$