Answer to Question #131915 in Differential Equations for Deema

Question

What is the degree and the order of this equation
y”y-(y’)^2=2

d^2y/dx^2 + 2dy/dx * d^3y/dx^3 +x=0

Answer 1

Order of a differential equation refers to the order of the highest derivative that exists in the equation.

The degree of a differential equation is the exponent of the highest order derivative involved in the differential equation when the differential equation satisfies the following conditions –

• All of the derivatives in the equation are free from fractional powers, positive as well as negative if any.
• There is no involvement of the derivatives in any fraction.
• There shouldn’t be involvement of highest order derivative as a transcendental function, trigonometric or exponential, etc. The coefficient of any term containing the highest order derivative should just be a function of x, y, or some lower order derivative.

In the first differential equation : y''y-(y')^2=2

Highest order derivative is y'', so order is 2 and its exponent is 1 so, degree is 1.

In the second differential equation : d^2y/dx^2 + 2dy/dx * d^3y/dx^3 +x=0 ,i.e. y''+2y'y'''+x=0

Highest order derivative is y''', so order is 3 and its exponent is 1 so, degree is 1.