If p and q are order and degree of differential equation y2((d2 y/d x2))2+3 x((d y/d x))1 / 3+x2 y2= sin x, then :

Question

If p and q are order and degree of differential equation y2((d2 y/d x2))2+3 x((d y/d x))1 / 3+x2 y2= sin x, then : (A) p>q (B) (p/q)=(1/2) (C) p=q (D)  p < q

Tardigrade Admin · Accepted Answer

y2((d2 y/d x2))2+x2 y2- sin x=-3 x((d y/d x))1 / 3 (y2((d2 y/d x2))2+x2 y2- sin x)3=-27 x3((d y/d x)) here order =2=p Degree =6=q ∴ p < q

Q. If $p$ and $q$ are order and degree of differential equation $y^{2} (\frac{d ^{2} y}{d x ^{2}})^{2} + 3 x (\frac{d y}{d x})^{1/3} + x^{2} y^{2} = sin x$ , then :

$p > q$

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

$p = q$

$p < q$

$y^{2} (\frac{d ^{2} y}{d x ^{2}})^{2} + x^{2} y^{2} - sin x = - 3 x (\frac{d y}{d x})^{1/3}$
$(y^{2} (\frac{d ^{2} y}{d x ^{2}})^{2} + x^{2} y^{2} - sin x)^{3} = - 27 x^{3} (\frac{d y}{d x})$
here order $= 2 = p$
Degree $= 6 = q$
$∴ p < q$

Q. If p and q are order and degree of differential equation y2(dx2d2y​)2+3x(dxdy​)1/3+x2y2=sinx, then :

p>q

qp​=21​

p=q

p<q