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  4. The order and degree of the differential equation [2(d2y/dx2)+((dy/dx))2](3/2)=(d3y/dx3) are respectively

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Q. The order and degree of the differential equation $\left[2\frac{d^{2}y}{dx^{2}}+\left(\frac{dy}{dx}\right)^{2}\right]^{\frac{3}{2}}=\frac{d^{3}y}{dx^{3}}$ are respectively

KEAMKEAM 2015Differential Equations

Solution:

$\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}=\frac{d^{3} y}{d x^{3}}$
On squaring both sides, we get
$\left[2 \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=\left(\frac{d^{3} y}{d x^{3}}\right)^{2}$
Hence, order is 3 and degree is 2 .