2. 3. au +- 4. +100 5. =0 6. Verify that the functions u(x,y)=x²-y2 and u(x,y) = e* sin y are solutions of the equation a?u a'u =D0 212

Calculus: Early Transcendentals
8th Edition
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Exercises-2.pdf
11.6 Exercises
Write down the order and degree of partial differential equations in problems 1-5.
au
=u?
ay
1.
a'u
au
2.
au
:0
ay
3.
4.
-100
3D0
5.
=0
6.
Verify that the functions u(x,y)=x2-y² and u(x,y) = er sin y are
solutions of the equation
a?u a?u
Examine whether cos (xy), e*y and (xy) are solutions of the partial differential equation.
xux - yuy = 0
Classify the partial differential equations as hyperbolic, parabolic, or elliptic.
8.
4 Uxx-7 Uxy + 3 uyy= 0
9.
4 Uxx-8 Uxy + 4 uyy= 0
10.
a? Uxx+2a Uxy +uyy = 0, az0
a²u
4
at?
a²u
a²u
=0
11.
:- 12
+9
a²u
12.
- 2
´ay²
For what values of x and y are the following partial differential equations
hyperbolic, parabolic, or elliptic?
13. Uxx+2xuxy+(1-y²) uyy=0
14. (1+y?) Ux+(1+x²) uyy=0
15
Uxx + x2 uw = 0
-2 sin x uxy – cos?x uy = 0
id the general solution of 2 ux-3 Uy = cos x
18. Solve ux+e'uy=y, u(0,y) = 1+y
Find the complete solutions of the equations in problem 19-25
19. p=(u +qyr
Transcribed Image Text:Exercises-2.pdf 11.6 Exercises Write down the order and degree of partial differential equations in problems 1-5. au =u? ay 1. a'u au 2. au :0 ay 3. 4. -100 3D0 5. =0 6. Verify that the functions u(x,y)=x2-y² and u(x,y) = er sin y are solutions of the equation a?u a?u Examine whether cos (xy), e*y and (xy) are solutions of the partial differential equation. xux - yuy = 0 Classify the partial differential equations as hyperbolic, parabolic, or elliptic. 8. 4 Uxx-7 Uxy + 3 uyy= 0 9. 4 Uxx-8 Uxy + 4 uyy= 0 10. a? Uxx+2a Uxy +uyy = 0, az0 a²u 4 at? a²u a²u =0 11. :- 12 +9 a²u 12. - 2 ´ay² For what values of x and y are the following partial differential equations hyperbolic, parabolic, or elliptic? 13. Uxx+2xuxy+(1-y²) uyy=0 14. (1+y?) Ux+(1+x²) uyy=0 15 Uxx + x2 uw = 0 -2 sin x uxy – cos?x uy = 0 id the general solution of 2 ux-3 Uy = cos x 18. Solve ux+e'uy=y, u(0,y) = 1+y Find the complete solutions of the equations in problem 19-25 19. p=(u +qyr
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