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  4. The degree of the differential equation[1+((dy/dx))2]3/2=l(d2y/dx2) is

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Q. The degree of the differential equation$\left[1+\left(\frac{dy}{dx}\right)^2\right]^{3/2}=l\frac{d^2y}{dx^2}$ is

Differential Equations

Solution:

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