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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
Partial Diff erential Equations 8-9
12. Form the partial differential equation of all planes through the
origin.
Ans: z = px + qy
8.5 FORMATION OF PARTIAL DIFFERENTIAL
EQUATIONS BY ELIMINATION OF ARBITRARY
FUNCTIONS
(a) Elimination of one arbitrary function of the form z = f (u)
where u = u(x, y, z)
Let
z = f (u) (8.45)
where f (u) is an arbitrary function of u where u = u(x, y, z) a known
function of x, y and z.
Differentiating (8.45) partially with respect to x and y
,
uu uu
pf p qf q
xz yz
⎛⎞
∂∂ ∂∂
⎛⎞
=⋅ + =⋅ +
′′
⎜⎟
⎜⎟
⎝⎠
∂∂ ∂∂
⎝⎠
(8.46), (8.47)
w
here on f denotes differentiation with respect to the ar
gument u.
Eliminating f from Eqs. (8.46)–(8.47) ...
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Publisher Resources

ISBN: 9781299487406Publisher Website