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

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

Taking square on both sides

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

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

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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order and degree

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