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i) E Ju(x, y) ду -2yu(x, y) = 0 You can solve it like an ordinary differential equation, treating a as a parameter. du(y) +2yu(y) = 0 Use the separation of variables method to find the solution u(x, y). u(y)=coexp(L To make u dependent of z, the only possibility is to consider co as dependent of z. Therefore, Find the general form of u(x, y): J2u(x, y) əx² +4u(x,y)=0 u(x, y) = co(r)exp du dr 2 where u = u(x,y)

i) E Ju(x, y) ду -2yu(x, y) = 0 You can solve it like an ordinary differential equation, treating a as a parameter. du(y) +2yu(y) = 0 Use the separation of variables method to find the solution u(x, y). u(y)=coexp(L To make u dependent of z, the only possibility is to consider co as dependent of z. Therefore, Find the general form of u(x, y): J2u(x, y) əx² +4u(x,y)=0 u(x, y) = co(r)exp du dr 2 where u = u(x,y)

Advanced Engineering Mathematics
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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8 Solution of Partial Differential Equations Find the general solution of the following partial differential equations. (Notice that the equations involve derivatives with respect to one variable only. You can solve it like an ordinary differential equation, treating the other variables as parameters. i) ii) iii) Ju(x, y) Əy +2yu(x, y) = 0 You can solve it like an ordinary differential equation, treating a as a parameter. +2yu(y) = 0 Use the separation of variables method to find the solution u(x, y). du(y) dy u(y) = coexp( To make u dependent of z, the only possibility is to consider co as dependent of z. Therefore, Find the general form of u(x, y): J²u(x, y) Əx² +4u(x, y) = 0 u(x, y) = co(r)exp( du əx = 2 where u = u(x, y)
Transcribed Image Text:8 Solution of Partial Differential Equations Find the general solution of the following partial differential equations. (Notice that the equations involve derivatives with respect to one variable only. You can solve it like an ordinary differential equation, treating the other variables as parameters. i) ii) iii) Ju(x, y) Əy +2yu(x, y) = 0 You can solve it like an ordinary differential equation, treating a as a parameter. +2yu(y) = 0 Use the separation of variables method to find the solution u(x, y). du(y) dy u(y) = coexp( To make u dependent of z, the only possibility is to consider co as dependent of z. Therefore, Find the general form of u(x, y): J²u(x, y) Əx² +4u(x, y) = 0 u(x, y) = co(r)exp( du əx = 2 where u = u(x, y)
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