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sql server reporting services barcode font DSolve dvnoarg : The function y appears with no arguments. in Software
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Encoding ANSI/AIM Code 128 In Java Using Barcode printer for Java Control to generate, create Code 128A image in Java applications. Painting GTIN  13 In None Using Barcode creator for Excel Control to generate, create EAN 13 image in Excel applications. DSolve[y'[x] x + y[x], y[x], x, GeneratedParameters mylabel] {{y[x] 1 x + x mylabel[1]}} Higher order differential equations are solved in a similar manner. The derivatives are represented as y'[x], y''[x], y'''[x], ... Alternatively, D, , or Derivative may be used. EXAMPLE 5
DSolve[y''[x]+ y [x] 0, y[x], x] {{y[x] C[1]Cos[x]+ C[2]Sin[x]}} C[1]Cos[x] + C[2]Sin[x]}} C[1]Cos[x]+ C[2]Sin[x]}} C[1]Cos[x]+ C[2]Sin[x]}} DSolve[D[y[x], {x, 2}]+ y[x] 0, y[x], x] {{y[x] DSolve[ {x, 2}y[x]+ y[x] 0, y[x], x] {{y[x] DSolve[Derivative[2][y][x]+ y[x] 0, y[x], x] {{y[x] More complicated differential equations are solved, if possible, using special functions. If Mathematica cannot solve the equation, it will return the equation either unsolved or in terms of unevaluated integrals. In such cases a numerical solution (see Section 11.2) may be more appropriate. Ordinary Differential Equations
d2y dy x2 2 + x + ( x 2 4) y = 0 is a special case of Bessel s equation. The solution is expressed in terms dx dx of Bessel functions of the first (BesselJ) and second (BesselY) kind. EXAMPLE 6
DSolve[x2 y''[x]+ x y'[x]+(x2 4)y[x] 0, y[x], x] {{y[x] BesselJ[2,x] C[1]+ BesselY[2,x] C[2]}} EXAMPLE 7
d 2 y dy + + y 2 = 0 is a nonlinear differential equation that Mathematica cannot solve. dx 2 dx DSolve[y''[x] + y'[x] + y[x]2 0, y[x], x] DSolve[[y[x]2 + y'[x] + y''[x] 0, y[x], x] If values of y, and perhaps one or more of its derivatives, are specified along with the differential equation, the task of finding y is known as an initial value problem. The differential equation and the initial conditions are specified as a list within the DSolve command. A unique solution is returned, provided an appropriate number of initial conditions are supplied. EXAMPLE 8 Solve the equation
dy = x + y with initial condition y(0) = 2. Then plot the solution. dx solution = DSolve[{y'[x] x + y[x], y[0] 2}, y[x], x] {{y[x] 1 + 3 x x}} Plot[y[x] /. solution, {x, 5, 2}, AxesOrigin
Here is another way the solution can be plotted: solution = DSolve[{y'[x] x + y[x], y[0] 2}, y, x] Function[{x}, 1 + 3 x x]}} f = solution[[1, 1, 2]]; Plot[f[x] {x, 5, 2}, AxesOrigin {0, 0}] , Ordinary Differential Equations
A useful way of visualizing the solution of a firstorder differential equation is to introduce the concept of a vector field. A vector field on 2 is a vector function that assigns to each point (x, y) a twodimensional vector F(x, y). By drawing the vectors F(x, y) for a (finite) subset of 2, one obtains a geometric interpretation of the behavior of F. VectorPlot[{Fx, Fy}, {x, xmin, xmax}, {y, ymin, ymax}] produces a vector field plot of the twodimensional vector function F, whose components are Fx and Fy. The direction of the arrow is the direction of the vector field at the point (x, y). The size of the arrow is proportional to the magnitude of the vector field. Axes Automatic may be used if axes are desired. By default, no axes are drawn. Frame False may be used if a frame around the plot is not desired. The default is Frame True. VectorScale is an option that determines the length and arrowhead size of the field vectors that are drawn. The default is ScaleFactor Automatic. Options include Tiny, Small, Medium and Large. Note: Starting with version 7, VectorPlot can be found in the Mathematica kernel. If you are using version 6, you must use VectorFieldPlot, located in the package VectorFieldPlots` which must be loaded prior to use. See the Documentation Center for appropriate usage.

