A differential equation is said to be of first degree if?
A
The highest order derivative is of order one
B
The highest order derivative appears to the first power only
C
The equation contains only one variable
D
The equation contains no derivatives
Analysis & Theory
First degree means the highest order derivative appears with power one (linearly).
Which of the following is a first-degree differential equation?
A
(dy/dx)² + y = 0
B
dy/dx + y = 0
C
(d²y/dx²)² + y = 0
D
y² + dy/dx = 0
Analysis & Theory
dy/dx + y = 0 has the derivative in first power only, so it is first degree.
The degree of dy/dx + y = 0 is?
A
0
B
1
C
2
D
Not defined
Analysis & Theory
The highest derivative is dy/dx with power 1, so degree = 1.
The equation (dy/dx)³ + y = 0 has degree?
A
1
B
2
C
3
D
Not defined
Analysis & Theory
The highest derivative is dy/dx and it appears with power 3, so degree = 3.
The equation (d²y/dx²) + (dy/dx)⁴ + y = 0 has degree?
A
1
B
2
C
3
D
4
Analysis & Theory
The highest derivative is d²y/dx² with power 1, but dy/dx has power 4. The overall degree is 4.
Which of the following is NOT first degree?
A
dy/dx + y = 0
B
(dy/dx)² + y = 0
C
d²y/dx² + 3 dy/dx + y = 0
D
dy/dx = x + y
Analysis & Theory
(dy/dx)² contains the derivative squared, so degree > 1.
The equation dy/dx = x² + y² is?
A
First order and first degree
B
First order and not first degree
C
Second order and first degree
D
Not a differential equation
Analysis & Theory
The highest derivative is dy/dx (order 1) and it appears to power 1 (degree 1).
The equation (d²y/dx²)² + dy/dx = 0 is?
A
Second order, first degree
B
Second order, second degree
C
Second order, not defined
D
First order, first degree
Analysis & Theory
The highest derivative is d²y/dx² with power 2, so order = 2 and degree = 2.
For the equation d³y/dx³ + y = 0, the degree is?
A
1
B
2
C
3
D
Not defined
Analysis & Theory
The highest derivative d³y/dx³ appears with power 1, so degree = 1.
The degree of a differential equation is not defined when?
A
It is linear in derivatives
B
It has polynomial in derivatives
C
Derivatives occur under radicals or fractions
D
It contains no derivatives
Analysis & Theory
Degree is not defined when derivatives appear under radicals or in denominators.