Let S denotes the set of real value functions of two variables z and y, whose partial derivatives of all orders exist. suppose u € S. Classify the following partial differential equations as:linear, quasi-linear or semi-linear; and homogeneous or non-homogeneous Table 1: You do not need to copy the table linear semi-linear quasi-linear homogeneous inhomogeneous equations 1 uu₂ + (x+y)uy + 3x² −y=e" 2 Mrrrarctan(z)+ Ryz sin(ry) 0 3 ZUy +1²U₂ = e² +² 4U+U₂y + √1+u²=0 (b) Explain why the following partial differential equation does not have any solution (you do not need to solve it). ²+²+1=0
Let S denotes the set of real value functions of two variables z and y, whose partial derivatives of all orders exist. suppose u € S. Classify the following partial differential equations as:linear, quasi-linear or semi-linear; and homogeneous or non-homogeneous Table 1: You do not need to copy the table linear semi-linear quasi-linear homogeneous inhomogeneous equations 1 uu₂ + (x+y)uy + 3x² −y=e" 2 Mrrrarctan(z)+ Ryz sin(ry) 0 3 ZUy +1²U₂ = e² +² 4U+U₂y + √1+u²=0 (b) Explain why the following partial differential equation does not have any solution (you do not need to solve it). ²+²+1=0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1.
Let S denotes the set of real value functions of two variables z and y, whose partial
derivatives of all orders exist. suppose u € S.
(a)
Classify the following partial differential equations as:linear, quasi-linear or
semi-linear; and homogeneous or non-homogeneous
Table 1: You do not need to copy the table
equations
1 uuz + (x + y)uy + 3x² − y = e"
| 2 | urrrarctan(r)+ursin(ry)=0
3
·uª
xu tru =e" +
U+ Uyy + √1 + u²=0
4
(b)
Explain why the following partial differential equation does not have any solution
(you do not need to solve it).
²+²+1=0
linear semi-linear quasi-linear || homogeneous inhomogeneous
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