The statement "If u, and u₂ are any solutions of a partial differential equation then so is cau, + pu₂ for all real numbers a and " is true only for some partial differential equations. For which of the following partial differential equations is the statement above true? e (I) (II) (III) d'u du +3. Ox² dy d'u dx² +11 du ду d du X ex ax = 0 du du + (IV) x² ² =0 + d²u Oy² = x² +1 0
The statement "If u, and u₂ are any solutions of a partial differential equation then so is cau, + pu₂ for all real numbers a and " is true only for some partial differential equations. For which of the following partial differential equations is the statement above true? e (I) (II) (III) d'u du +3. Ox² dy d'u dx² +11 du ду d du X ex ax = 0 du du + (IV) x² ² =0 + d²u Oy² = x² +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:The statement "If u₁ and u₂ are any solutions of a partial
differential equation then so is au + Bu₂ for all real numbers
a and ß" is true only for some partial differential equations.
For which of the following partial differential equations is the
statement above true?
e
(I)
(II)
(III)
(IV)
d'u du
+3 =0
dy
Ox²
d'u du
+11
ox² dy
d
du
Ox
Əx
d²u du
Ox²
= 0
+
dzu
Oy²
<=0
+ = x² +1
Oy,²
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