
3.5. Equations Containing Hyperbolic F unctions and Arbitrary Parameters 351
5.
∂w
∂t
= a
∂
2
w
∂x
2
+ (b sinh
k
ωt + c)
∂w
∂x
.
This is a special case of equation 3.8.2.1 with f (t) = b sinh
k
ωt + c.
6.
∂w
∂t
= a
∂
2
w
∂x
2
+ x(b sinh
k
ωt + c)
∂w
∂x
.
This is a special case of equation 3.8.2.3 with f (t) = b sinh
k
ωt + c.
7.
∂w
∂t
= a
∂
2
w
∂x
2
+ b
∂w
∂x
+ (c sinh
k
ωt + s)w.
This is a special case of equation 3.8.3.1 with f (t) = b and g(t) = c sinh
k
ωt + s.
8.
∂w
∂t
= a
∂
2
w
∂x
2
+
cx sinh
k
ωt +
b
x
∂w
∂x
.
This is a special case of equation 3.8.2.6 with f (t) = c sinh
k
ωt.
9.
∂w
∂t
= ax
∂
2
w
∂x
2
+ (bx sinh
k
ωt + c)w.
This is a special case of equation 3.8.4.1 with f (t) = b sinh
k
ωt and g(t) = c.
10.
∂w
∂t
= ax
2