problemset1

# 0 ay 15 10 05 00 0 1 2 3 4 5 6 ax g x0

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Unformatted text preview: ∗ x] Tan[ax] Integrate[g [x], x] o − Log[Ca s[ax]] DSolve[y � [x] == Tan[a ∗ x] ∗ (Cosh[a ∗ (y [x] − d)] − Cosh[a ∗ y [x]])/(Sinh[a ∗ d] + Sinh[a ∗ (y [x] − d)]− Sinh[a ∗ y [x]]), y , x] Solve:�tdep : The equations appear to involve the variables to be solved for in an essentially � on-algebraic way.�� : n 2ArcTanh[Cosh[a]−Sinh[a]Tanh[ 1 ay [x]]]Cosh[a] 2 2ie Cos[ax](Cosh[a(−2+y [x])]−Cosh[ay [x]]) Solve − == C [1], y [x] a Ex ExT = −Cos[xT] ∗ (1 + (Sinh[yT − dT] − Sinh[yT])/Sinh[dT]) −Cos[xT](1 + Csch[2](−Sinh[2 − yT] − Sinh[yT])) Ey EyT = −Sin[xT] ∗ (Cosh[yT − dT] − Cosh[yT])/Sinh[dT] −(Cosh[2 − yT] − Cosh[yT])Csch[2]Sin[xT] dT = 2 2 LoadVectorFieldPlots ` Pl Pi plot1 = PlotVectorField[{ExT, EyT}, {xT, 0, 2 ∗ Pi}, {yT, 0, dT}, Frame → True, FrameLabel → {ax, ay}] 2.0 ay 1.5 1.0 0.5 0.0 0 1 2 3 4 ax Pi plot2 = {GrayLevel[.8], Rectangle[{0, 0}, {2 ∗ Pi, dT}]} {GrayLevel[0.8], Rectangle[{0, 0}, {2π , 2}]} Show[Graphics[plot2], plot1, Frame → True, FrameLabel...
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