The order and degree of the differential equation  \left ( 1+3\frac{dy}{dx} \right )^{\frac{2}{3}}=4\frac{d^{3}y}{dx^{3}}   are

  • Option 1)

    1,\frac{2}{3}\;

  • Option 2)

    \; \; 3,1\;

  • Option 3)

    \; 3,3\;

  • Option 4)

    \; 1,2

 

Answers (1)

As we learnt in 

Order of a Differential Equation -

The order of a differential equation is order of highest order occuring in differential equation

- wherein

order of

\frac{d^{2}y} {dx^{2}}+5=0  

is 2.

 

 

 and

 

Degree of a Differential Equation -

Degree of Highest order differential coefficient appearing in it, provided it can be expressed as a polynomial equation in derivatives

- wherein

\left ( \frac{dy}{dx} \right )^{2}+3\left ( \frac{dy}{dx} \right )-5=0

Degree = 2

 

  \dpi{100} \left ( 1+3\frac{dy}{dx} \right )^{\frac{2}{3}}=4\frac{d^{3}y}{dx^{3}}

\dpi{100} \left ( 1+3\frac{dy}{dx} \right )^{2}= \left( 4\:.\:\frac{d^{3}y}{dx^{3}} \right )^{3}

\therefore Order=3

Degree=3

 

 


Option 1)

1,\frac{2}{3}\;

This option is incorrect.

Option 2)

\; \; 3,1\;

This option is incorrect.

Option 3)

\; 3,3\;

This option is correct.

Option 4)

\; 1,2

This option is incorrect.

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