Question

用mathematica求解如下二阶微分方程的数值解 输出最终的数值解并画图

用mathematica求解如下二阶微分方程的数值解和画图的程序代码
A*y (x) =
y'' (x)/{{1 + [y' (x)]^2}^(3/2)} +
y' (x)/{{1 + [y' (x)]^2}^(1/2)}
其中A＝134708。边界条件 : 1) y' (0) = 0; 2) y' (0.005) = cot58 (58 是角度)
x={0, 0.005}, 步长是0.0001

Answer 1

In[1]:=s = NDSolve[{134708*y[x] ==
y''[x]/(1 + (y'[x])^2)^1.5 + y'[x]/(1 + (y'[x])^2)^0.5,
y'[0] == 0, y'[0.005] == Cot[58*\[Pi]/180]}, y, {x, 0, 0.005}]
Plot[Evaluate[y[x] /. s], {x, 0, 0.005}, PlotRange -> All]
esol = Block[{\[Epsilon] = $MachineEpsilon},
NDSolve[{134708*y[x] ==
y''[x]/(1 + (y'[x])^2)^1.5 + y'[x]/(x*(1 + (y'[x])^2)^0.5),
y'[\[Epsilon]] == 0, y'[0.005] == Cot[58*\[Pi]/180]},
y, {x, \[Epsilon], 0.005}]]
Plot[Evaluate[y[x] /. esol], {x, 0.00001, 0.005}, PlotRange -> All]