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  • The degree of the differential equation is (A) 3 (B) 2 (C) 1 (D) not defined

11.    The degree of the differential equation \left(\frac{d^2y}{dx^2} \right )^3 + \left(\frac{dy}{dx} \right )^2 + \sin\left(\frac{dy}{dx}\right ) + 1= 0 is

            (A)    3

            (B)    2

            (C)    1

            (D)    not defined

Answers (1)

best_answer

Given function is
\left(\frac{d^2y}{dx^2} \right )^3 + \left(\frac{dy}{dx} \right )^2 + \sin\left(\frac{dy}{dx}\right ) + 1= 0
We can rewrite it as
(y^{''})^3+(y^{'})^2+\sin y^{'}+1=0
Now, it is clear from the above that, the highest order derivative present in differential equation is  y^{''}

Therefore, order of given differential equation  \left(\frac{d^2y}{dx^2} \right )^3 + \left(\frac{dy}{dx} \right )^2 + \sin\left(\frac{dy}{dx}\right ) + 1= 0    is  2
Now, the given differential equation is  a not  polynomial equation in it's derivatives  
Therefore, it's  degree is not defined

Therefore, answer is (D)

Posted by

Gautam harsolia

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