Find the order and the degree of the differential equation  x^2\frac{\mathrm{d^2y} }{\mathrm{d} x^2}=\left \{ 1+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^2 \right \}^4.

 

 

 

 

 
 
 
 
 

Answers (1)

x^2\frac{\mathrm{d^2}y }{\mathrm{d} x^2}=\left \{ 1+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^2 \right \}^4

x^2\frac{\mathrm{d^2}y }{\mathrm{d} x^2}=\left [ 1+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^2 \right ]^2 \times \left [ 1+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^2 \right ]^2

x^2\frac{\mathrm{d^2}y }{\mathrm{d} x^2}=\left [ 1+2\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^2+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^4 \right ] \cdot \left [ 1+2\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^2+\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^4 \right ]

\therefore  Highest order derivative =\frac{\mathrm{d^2}y }{\mathrm{d} x^2}

\Rightarrow Order=2

Degree of differential equation = degree of highest order derivative

Degree= 1

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