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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
1.3. Equations of the Form f(x, y)
∂w
∂x
+ g(x, y)
∂w
∂y
= h(x, y)w 103
7. a
∂w
∂x
+ b
∂w
∂y
=

c cos(λx) + k cos(µy)

w.
General solution: w = exp
c
sin(λx) +
k
sin(µy)
Φ(bx ay).
8. x
∂w
∂x
+ y
∂w
∂y
= ax cos(λx + µy)w.
General solution: w = exp
ax
λx + µy
sin(λx + µy)
Φ
y
x
.
9. a
∂w
∂x
+ b cos
n
(λx)
∂w
∂y
=

c cos
m
(µx) + s cos
k
(βy)

w.
This is a special case of equation 1.3.7.33 with f (x) = a, g
1
(x) 0, g
0
(x) = b cos
n
(λx),
and h(x, y) = c cos
m
(µx) + s cos
k
(βy).
10. a
∂w
∂x
+ b cos
n
(λy)
∂w
∂y
=

c cos
m
(µx) + s cos
k
(βy)

w.
This is a special case of equation 1.3.7.19 with f (x) = a, g(y) = b cos
n
(λy), h
1
(x) =
c cos
m
(µx), and h
2
(y) = s cos
k
(βy).
Coefficients of equations contain ...
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Publisher Resources

ISBN: 9781466581494