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Degree of differential equation

\left ( \frac{d^{2}y}{dx^{2}} +1 \right )^{1/3}= \left ( \frac{dy}{dx} \right )^{1/2} is

  • Option 1)

    1

  • Option 2)

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  • Option 4)

    4

 

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As we learnt

 

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

 

 Currently it is not in form of polynomial equation in derivative.So we will raise to the minimum exponent.so that it is converted to required form,so we will raise to exponent 6. i.e.

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

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

Now,we can say degree =2.


Option 1)

1

Option 2)

2

Option 3)

3

Option 4)

4

Posted by

Himanshu

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