Question

Find the order and degree of the following differential equations

a)      D^y/dx^3+6d^2y/dx+11dy/dx+6y=0

b)     (D^3y/dx^3)^2-3d^2y/dx^2+4y=0

c)      (1-x^2)dy/dx-xy=1

d)     2d^2y/dx^2-3dy/dx+y=0

Answer 1

The ORDER of an ODE is the highest derivative in the equation

The DEGREE of an ODE is the power of the highest derivative in the equation

(a) Highest derivative is $\frac{d³y}{dx³}$. Thus, the order is 3.

The power of the highest derivative is 1. Hence, the degree is 1

(b) Highest derivative is $\frac{d³y}{dx³}$ . Thus, the order is 3.

The power of the highest derivative is 2. Hence, the degree is 2

(c) Highest derivative is $\frac{dy}{dx}$ . Thus, the order is 1.

The power of the highest derivative is 1. Hence, the degree is 1.

(d) Highest derivative is $\frac{d²y}{dx²}$ . Thus, the order is 2.

The power of the highest derivative is 1. Hence, the degree is 1