
356 SECOND-ORDER PARABOLIC EQUATIONS WITH ONE SPACE VARIABLE
3.7 Equations Containing Trigonometric Functions and
Arbitrary Parameters
3.7.1 Equations Containing a Cosine
1.
∂w
∂t
= a
∂
2
w
∂x
2
+ (b cos
k
ωt + c)w.
This is a special case of equation 3.8.1.1 with f (t) = b cos
k
ωt + c.
2.
∂w
∂t
= a
∂
2
w
∂x
2
+ (b cos
k
ωt + cx)w.
This is a special case of equation 3.8.1.6 with f (t) = c and g(t) = b cos
k
ωt.
3.
∂w
∂t
= a
∂
2
w
∂x
2
+ x(b cos
k
ωt + c)w.
This is a special case of equation 3.8.1.3 with f (t) = b cos
k
ωt + c.
4.
∂w
∂t
= a
∂
2
w
∂x
2
+ (c cos
k
ωt − bx
2
)w.
This is a special case of equation 3.8.1.7 with f (t) = c cos
k
ωt.
5.
∂w
∂t
= a
∂
2
w
∂x
2
+ (b cos
k
ωt + c)
∂w
∂x
.
This is a special case of equation ...