Write the order and the degree of the differential equation
  \left ( \frac{d^{4}y}{dx^{4}} \right )^{2}= \left [ x+\left ( \frac{dy}{dx} \right ) ^{2}\right ]^{3}

 

 

 

 
 
 
 
 

Answers (1)

given:\left ( \frac{d^{4}y}{dx^{4}} \right )^{2}= \left [ x+\left ( \frac{dy}{dx} \right ) ^{2}\right ]^{3}
          \left ( \frac{d^{4}y}{dx^{4}} \right )^{2}= x^{3}+\left ( \frac{dy}{dx} \right )^{6}+3x^{2}\left ( \frac{dy}{dx} \right )^{2}+3x\left ( \frac{dy}{dx} \right )^{4}
The order of the highest derivative is 4 so its order is 4.

The power of the highest order of the derivative is 2 so the degree of the differential equation is 2.

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