Question

The degree of the differential equation[1+(dy/dx)³]²/³=x(d²y/dx²) is........,Select correct option from given options.
(a) 3
(b) 2
(c) 6
(d) 1

Answer 1

degree of given differential equation is 3

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

The degree of the differential equation

$\displaystyle \sf{ { \bigg[1 + { \bigg( \frac{dy}{dx} \bigg)}^{3} \bigg] }^{ \frac{2}{3} } = x \bigg( \frac{ {d}^{2}y }{d {x}^{2} } \bigg)\: }$

DEFINITION TO BE MEMORISED

DIFFERENTIAL EQUATION

A differential equation is an equation which involves differential coefficients or differentials

ORDER OF A DIFFERENTIAL EQUATION

The order of a differential equation is the order of the highest derivative appearing in it.

DEGREE OF A DIFFERENTIAL EQUATION

The degree of a differential equation is the degree of the highest derivative occuring in it after the equation has been expressed in a form free from radicals and fractions as far as the derivatives are concerned

CALCULATION

The given differential equation is

$\displaystyle \sf{ { \bigg[1 + { \bigg( \frac{dy}{dx} \bigg)}^{3} \bigg] }^{ \frac{2}{3} } = x \bigg( \frac{ {d}^{2}y }{d {x}^{2} } \bigg)\: }$

Which can be rewritten as

$\displaystyle \sf{ { \bigg[1 + { \bigg( \frac{dy}{dx} \bigg)}^{3} \bigg] }^{ 2 } = {x}^{3} { \bigg( \frac{ {d}^{2}y }{d {x}^{2} } \bigg)}^{3} \: }$

Here the differential equation involves highest derivative of order 3

Hence the order of the given differential equation is 2

Also the degree of the highest derivative occuring in the differential equation is 3

Hence the degree of the given differential equation is 3

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LEARN MORE FROM BRAINLY

The order and degree of the differential equation of the family of parabolas having vertex at origin and axis along positive x-axis

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