What is the degree of the differential equation \left(\frac{d^{2}y}{dx^{2}}\right)^{\frac{3}{2}}=\left(\frac{dy}{dx}\right)^{\frac{5}{2}}?

Explanation

Square both sides to remove the fractional powers: \left(\frac{d^2y}{dx^2}\right)^3 = \left(\frac{dy}{dx}\right)^5. The degree of a differential equation is the highest power of the highest order derivative after it has been made free from radicals and fractions. The highest order derivative is \frac{d^2y}{dx^2}, and its power is 3.

Related questions on Calculus

• Let z=[y] and y=[x]-x, where [.] is the greatest integer function. If x is <strong>NOT</strong> an integer but positive, then what i...
• If f(x)=4x+1 and g(x)=kx+2 such that fog(x)=gof(x), then what is the value of k?
• What is the <strong>MINIMUM</strong> value of the function f(x)=\log_{10}(x^{2}+2x+11)?
• What is \int(x^{x})^{2}(1+\ln x)\,dx equal to ?
• What is \int e^{x}\{1+\ln x+x\ln x\}\,dx equal to?