Sues tion We have a Cinear equation; yux- xuy =0 Initial condition is; u(x1 y-s) =s that is *0, s) = Xols)1y (0, s) =yols)=s, ulo,s) - Uols) -s 1tind the characteristic equations! alx, y,ulux+ b(x,y,uluy-c (x,y,u) alx,y, u) 4) dt blx.y,ul. 12) %3D dt = c(x, y,u) dt → Integrate equations 1-2) using initial equations. Find the solutions clearly interms of t ands. → Integrate equation (3) using initial equ ations. clearly t and s. Tind the solution interms of → Tind the implicit expression relating the solution u and X,y. Also write the solution U intems of X ond 9iulx,y) explcity.

Sues tion We have a Cinear equation; yux- xuy =0 Initial condition is; u(x1 y-s) =s that is *0, s) = Xols)1y (0, s) =yols)=s, ulo,s) - Uols) -s 1tind the characteristic equations! alx, y,ulux+ b(x,y,uluy-c (x,y,u) alx,y, u) 4) dt blx.y,ul. 12) %3D dt = c(x, y,u) dt → Integrate equations 1-2) using initial equations. Find the solutions clearly interms of t ands. → Integrate equation (3) using initial equ ations. clearly t and s. Tind the solution interms of → Tind the implicit expression relating the solution u and X,y. Also write the solution U intems of X ond 9iulx,y) explcity.

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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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

Que
uestion
We have a linear equatHon yux- xuy=0
Initial condition is ; ul x =1, y-s) S
that is
*, s1= Xls)=1,y (0,5)=4o(5)=s, ulo,s) - Uols) =s
JFind the characteristic equations:
alx, y,ulux+ b(x,y,uluy = c (x,y;u)
alx,y,u)
dt
dy
blx.y,ul.--
(2)
%3D
du
c(x, y,u)
(3 )
dt
→ Integrate equations 1-2) using initial equations.
Find the solutions clearly interms of t ands.
→ Integrate equation (3) using initial equ ations.
Tind the solution clearly int erms of
t and s
→ Tind the implicit expression relating the solution u and
intens of x and
X,y. Also write the solutionu
yiulx,y) explueity.

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