Practical-3

Q1. Solve the linear P.D.E 2p+3q+z=0.

z := u@x, yD;p :=D@u@x, yD, xD;q :=D@u@x, yD, yD;eqn := 2 p + 3 q + z 0;

sol =DSolve@eqn, u@x, yD, 8x, y>

particularsolution = u@x, yD . sol@@1DD . C@1D@t_D Sin@tD

-x2

SinB1

2

H-3 x + 2 yLF

Plot3D@particularsolution, 8x, -5, 5

Q2.Solve the first order cauchy

Problem,

ux+ xu

y= 0, with the Cauchy data uH0, yL= Sin y.

p :=D@u@x, yD, xD;q :=D@u@x, yD, yD;eqn := p + x q 0;

sol = u@x, yD . DSolve@8eqn, u@0, yD Sin@yD

Plot3DAx2 - y + 2 x y + y2, 8x, -1.85883, 1.85883