Write order and degree (if defined)of differential equations: (d^2y/dx^2)+y^2+e^(dy/dx)=0

Question

Write order and degree (if defined)of differential equations: 

\(\cfrac{d^2y}{dx^2}+y^2+e^{({dy/dx})}=0\)

(d²y/dx²)+y²+e^(dy/dx)=0

Answer 1

The order of a differential equation is the order of the highest derivative involved in the equation. So the 

order comes out to be 2 as we have \(\cfrac{d^2y}{dx^2}\) and the degree is the highest power to which a derivative is raised. 

But here when we open the series of \(e^x\) as \(1+\cfrac{x}{1!}+\cfrac{x^2}{2!}+\cfrac{x^3}{3!}+------\) . Also, the equation has to be polynomial. Therefore the degree is not defined. Also, the equation has to be a polynomial, but opening the exponential function will give undefined power to the highest derivative, so the degree of this function is not defined. 

So the answer is 2, not defined .

Answer 2

Order - highest order derivative

Degree - Power of highest order derivative

So, order = 2 (Clear from the question)

The degree is not defined as e^dy/dx can be expanded using series expansion [e^x = 1 + x + x²/2 + ...] and so the power of highest derivative which is power of dy/dx goes to infinity. Thus, degree is not defined.