The order of a differential equation is defined as?
A
The highest power of the independent variable
B
The highest order derivative present
C
The total number of derivatives present
D
The degree of the equation
Analysis & Theory
The order is the order of the highest derivative present in the equation.
The degree of a differential equation is defined as?
A
The highest exponent of the variable
B
The power of the highest order derivative after clearing radicals and fractions
C
The number of terms in the equation
D
The total number of derivatives present
Analysis & Theory
Degree is the power of the highest order derivative, provided the equation is polynomial in derivatives.
Find the order of the differential equation: d²y/dx² + dy/dx + y = 0
Analysis & Theory
The highest derivative is d²y/dx², so the order is 2.
Find the degree of the equation: (d²y/dx²)³ + dy/dx = 0
Analysis & Theory
The highest order derivative is d²y/dx², and its power is 3, so the degree is 3.
What is the order of dy/dx + y = 0?
Analysis & Theory
The highest derivative is dy/dx, so the order is 1.
Find the degree of dy/dx + y = 0
Analysis & Theory
The highest order derivative is dy/dx with power 1, so degree = 1.
The equation: d³y/dx³ + (d²y/dx²)² + y = 0 has order?
Analysis & Theory
The highest derivative is d³y/dx³, so the order is 3.
The degree of d³y/dx³ + (d²y/dx²)² + y = 0 is?
Analysis & Theory
The highest order derivative is d³y/dx³ with power 1, so degree = 1.
If the equation contains derivatives under a radical (like √(dy/dx)), then degree is?
Analysis & Theory
Degree is not defined if the equation is not polynomial in derivatives.
In the equation (d²y/dx²) + (dy/dx)⁴ = 0, the order and degree are?
Analysis & Theory
Highest derivative is d²y/dx² (order 2) and its power is 1. But the highest power of derivatives in the equation is 4 from (dy/dx)⁴, so degree = 4.