Section 1.1 Worksheet MAT–283 Di↵erential Equations
State the order of the given ordinary di↵erential equation. Determine whether the equation is linear or
nonlinear.
s ✓ ◆2
1. (1 x)y 00 4xy 0 + 5y = cos(x) d2 y dy
5. 2
= 1+
dx dx
linear 2nd order
nonlinear
✓ ◆4
d3 y
2. x 3
dx
dy
dx
a+ y = 0 d2 R k
6. =
dt2 R2
nonlinear linear and order
3. t5 y (4) t3 y 00 + 6y = 0
3ʳᵈ
7. sin(✓)y 000 cos(✓)y 0 = 2
linear 4th linear
4.
d2 u du
+ + u = cos(r + u)
nonlinear
8. x
and
00
"
1
(x0 )
2
#
x0 + x = 0
dr2 dr 3
linear and nonlinear
State the order of the given ordinary di↵erential equation. Determine whether the equation is linear or
nonlinear.
s ✓ ◆2
1. (1 x)y 00 4xy 0 + 5y = cos(x) d2 y dy
5. 2
= 1+
dx dx
linear 2nd order
nonlinear
✓ ◆4
d3 y
2. x 3
dx
dy
dx
a+ y = 0 d2 R k
6. =
dt2 R2
nonlinear linear and order
3. t5 y (4) t3 y 00 + 6y = 0
3ʳᵈ
7. sin(✓)y 000 cos(✓)y 0 = 2
linear 4th linear
4.
d2 u du
+ + u = cos(r + u)
nonlinear
8. x
and
00
"
1
(x0 )
2
#
x0 + x = 0
dr2 dr 3
linear and nonlinear
