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order and degree

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



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