# Degree of a differential equation doubt

What should be the degree of this differential equation 1 or 2 $$\frac{d^2x}{dy^2}+\sqrt{1+\left(\frac{dx}{dy}\right)^3}=0$$

As per definition: the degree of a differential equation is the power of highest differential coefficient, which appearing in the given equation, when the differential coefficients are free from radicals and fractions. So I think I should remove the radical in the equation above and the degree will be 2. Is it correct ?

• You might want to edit. I'm not seeing "the equation above". – bob.sacamento Dec 3 '15 at 17:15
• Its given in the image – Onix Dec 3 '15 at 17:16
• If you mean the order, it's a second order differential equation. – gerd Dec 3 '15 at 17:23
• Degree is different to Order as he defined in the question. – Ian Miller Dec 3 '15 at 17:25
• I think that you mean it's order. Its ODE classification: It is a second- order nonlinear ordinary differential equation – Jan Dec 3 '15 at 17:43

$$\left(\frac{d^2y}{dx^2}\right)^2=1+\left(\frac{dy}{dx}\right)^3$$