order and degree

by

differential equations

Solutions of examples.

In this post we will provide the solution of two examples i.e order and degree of differential equations given below

 

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

 

                                          Taking square on both sides

 \left [1+ \left (\frac{dy}{dx} \right )^2 \right ]^{3/2 \times 2}=\left (\frac{d^2y}{dx^2} \right )^2\\ =\left [1+ \left (\frac{dy}{dx} \right )^2 \right ]^{3}=\left (\frac{d^2y}{dx^2} \right )^2 \\ \Rightarrow order=02\\ \Rightarrow degree=02\\

 

 

 

 

  1. \frac{dy}{dx} +\left [1+ \left (\frac{dy}{dx} \right )^2 \right ]^{3/2}=0

       

                                            Taking square on both sides

 

\left (\frac{dy}{dx} \right )^2 +\left [1+ \left (\frac{dy}{dx} \right )^2 \right ]^{3/2 \times 2}=0\\ \,\,\ \left (\frac{dy}{dx} \right )^2 +\left [1+ \left (\frac{dy}{dx} \right )^2 \right ]^{3}=0\\

Now open cube then we get

order =     01

degree =  06

 

 

Do you read the related definitions of Differential Equations.then Click Here

 

 

 

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