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Solve PDEs over 3D Regions&Make a
from .In[1]:=Xmr = BoundaryDiscretizeGraphics[
ExampleData[{&Geometry3D&, &SpaceShuttle&}]];Solve a Laplace equation over the orbiter of the Space Shuttle.In[2]:=Xuif = NDSolveValue[{Inactive[Laplacian][u[x, y, z], {x, y, z}] == 0,
DirichletCondition[u[x, y, z] == 1, z &= -1.3],
DirichletCondition[u[x, y, z] == 0, x &= -7.]},
u, {x, y, z} \[Element] mr];Visualize the solution using the show complete Wolfram Language inputhide inputIn[3]:=XNeeds[&NDSolve`FEM`&]
ElementMeshSurfacePlot3D[uif, Boxed -& False, ViewPoint -& {0, -4, 2}]Out[3]=
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Find Symbolic Solutions for Delay Differential Equations&Solve a first-order delay equation using .In[1]:=Xsol = DSolve[{x'[t] == x[t - 1]^2, x[t /; t & 0] == a t},
x[t], {t, 0, 2}]Out[1]=In[2]:=XPlot[Evaluate[Table[x[t] /. sol[[1]], {a, 1, 5}]], {t, -1, 2},
Exclusions -& None]Out[2]=Solve a fifth-order delay equation.In[3]:=Xsol = DSolve[{x'''''[t] == -x[t - 2], x[t /; t &= 0] == a t},
x, {t, 0, 10}];In[4]:=XPlot[Evaluate[Table[x[t] /. sol[[1]], {a, 1, 4, 1/3}], {t, -1, 10}],
WorkingPrecision -& 400, PlotRange -& All, Exclusions -& None]Out[4]=Solve a system of delay equations.In[5]:=Xeqns = {x'[t] == a y[t - 1] + y[t - 3], y'[t] == x[t - 1],
x[t /; t &= 0] == t, y[t /; t &= 0] == t^2};In[6]:=Xsol = DSolve[eqns, {x, y}, {t, 0, 5}];In[7]:=XParametricPlot[
Evaluate[Table[{x[t], y[t]} /. sol, {a, -1, 2, 1/3}]], {t, 0, 5},
WorkingPrecision -& 200, Exclusions -& None]Out[7]=
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Enable JavaScript to interact with content and submit forms on Wolfram websites.mathematica 微分方程 e_百度知道
mathematica 微分方程 e
用Mathematica解微分方程，程序把它写成了近似值的小数，如何能使该答案仍旧以e的指数形式表达？另外程序出来的答案如何代回去进行检验，答案有e的指数
我有更好的答案
C2为任意常数.Cosh(C1) = (e^(C1) + e^(-C1))/2Sinh(C1) = (e^(C1) - e^(-C1))/[x]^2], y[x], x]{{y[x] -&gt。 刚刚你的图片没有显示; x^2/2 + C[1]}}, x]
按 shift + enter 运行：{{y[x] -&[x] == Sqrt[1 + y&#39：DSolve[2 x*y'' = x 命令为：DSolve[y&#39解决常微分问题，命令是 DSolve，可以看到更多例子，了解该命令的更多细节，举个例子：y '3 Sqrt[x] ((-3 + x) Cosh[C[1]] + (3 + x) Sinh[C[1]])}} y = C2 + 1&#47.你可以照着这个例子解决自己需要的问题，按 F1 可以按出帮助菜单，输入 DSolve 搜索;[x] == x, y' C[2] + 1/3 √x * ((x-3)*Cosh(C1) + (x+3)*Sinh(C1))，C1;[x].结果为
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我们会通过消息、邮箱等方式尽快将举报结果通知您。各位大神，请问一下这个微分方程怎么解不出来【mathematica吧】_百度贴吧
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各位大神，请问一下这个微分方程怎么解不出来收藏
各位大神，请问一下这个微分方程怎么解不出来DSolve[{X'[i] - 10*Y[i] - 10*X[i] == 0,
Y'[i] - 28*X[i] + X[i]*Z[i] + Y[i] == 0,
Z'[i] - X[i]*Y[i] + 8*Z[i]/3 == 0}, {X[i], Y[i], Z[i]}, i]运行的结果是这样的哪里出问题了？？
首先，不需要动不动就喊大神，这个真担不起。大家都是同道中人而已，见识过stackoverflow上的牛人，知道离大神差的很远，喊我大神我也不会觉得高兴，真没有必要。下面回答LZ的问题。首先，微分方程组有多种分类，最简单的就是线性常系数的，例如 A = {{4, -6}, {1, -1}}; X[t_] = {x[t], y[t]}; system = X'[t] == A.X[t]; 之类的，例子就是教程中的。DSolve对此类微分方程组支持的较好；其次是线性变系数微分方程组，按照教程中的说法，DSolve只能支持系数矩阵具有简单形式的方程组；最后是非线性方程组，这个求解通解的DSolve受到的限制就更大，稍微复杂点的形式就不用指望能得到解析通解了。下面简单分析LZ提出的微分方程组，可以发现，在第二和第三个方程中有X[i]*Z[i]和X[i]*Y[i]项，这说明这个微分方程组是非线性的，而且三个变量之间耦合极深，求解析通解已经不可能，因此DSolve无法处理，只能返回未计算结果。如果把上述非线性项去除乘号，改为加减法，那么方程组类型就变为线性的，DSolve就可以处理了。或者可以使用NDSolve，进行数值求解，只要有初值，这比硬求解析通解要简单得多。最后的结论就是，微分方程组的解决依赖于自身的数学水平，mathematica只能是工具，无法超越现行的数学理论。因此，要将这一工具用好，我们大家都需要提高自身的数学水平。
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& PDEs and Finite ElementsVersion 10 extends its numerical differential equation-solving capabilities to include the finite element method. Given a PDE, a domain, and boundary conditions, the finite element solution process—including grid and element generation—is fully automated. Stationary and transient solutions to a single PDE or a system of partial differential equations are supported for one, two, and three dimensions. Solve partial differential equations over arbitrarily shaped regions. Solve stationary and transient PDEs in one, two, and three dimensions.Solve coupled systems of PDEs. Specify Dirichlet boundary conditions. Specify generalized Neumann and Robin values. Support for linear PDEs with coefficients that are variable in time and space. Freely formulate coupled PDEs for multiphysics analysis.Specify domains using the full geometric region framework. Fully automatic mesh generation from any region. Obtain solutions as approximate functions that can be further analyzed. Full suite of intermediate-level data structures and solution functions for detailed control and analysis of the solution. Support for explicit mesh generation.Support for meshes with first- and second-order interpolation.Support for meshes with curved boundaries.
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