Partial Differential equation
3
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:= 2p + 3q + z 0; sol = DSolve@eqn, u@x,yD, 8x,y<D ::u@x, yD fiª -x2 C@1DB 1 2 H-3x + 2yLF>> particularsolution = u@x,yD. sol@@1DD .C@1D@t_D fi Sin@tD ª -x2 SinB 1 2 H-3x + 2yLF Plot3D@particularsolution, 8x, -5, 5<, 8y, -5, 5<, PlotPoints fi 50D -5 0 5 -5 0 5 -4 -2 0 2 4
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Contains Mathematica generated practicals for undergrads of mathematics on Partial Differential Equation
Transcript of Partial Differential equation
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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
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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