DSOLVE象征性的常微分方程的解决方案。DSOLVE不会接受方程作为字符串在未来版本。使用符号表达式或符号对象。例如,使用对称y (t);dsolve (diff (y) = = y)而不是dsolve (Dy = y)。DSOLVE (eqn1 eqn2,…)接受符号方程代表常微分方程和初始条件。默认情况下,自变量是“t”。独立变量可能改变从“t”到其他一些符号变量,包括变量作为输入参数。DIFF函数构造衍生品的符号函数(见信谊/ symfun)。初始条件涉及衍生品必须使用一个中间变量。 For example, syms x(t) Dx = diff(x); dsolve(diff(Dx) == -x, Dx(0) == 1) If the number of initial conditions given is less than the number of dependent variables, the resulting solutions will obtain arbitrary constants, C1, C2, etc. Three different types of output are possible. For one equation and one output, the resulting solution is returned, with multiple solutions to a nonlinear equation in a symbolic vector. For several equations and an equal number of outputs, the results are sorted in lexicographic order and assigned to the outputs. For several equations and a single output, a structure containing the solutions is returned. If no closed-form (explicit) solution is found, then a warning is given and the empty sym is returned. DSOLVE(...,'IgnoreAnalyticConstraints',VAL) controls the level of mathematical rigor to use on the analytical constraints of the solution (branch cuts, division by zero, etc). The options for VAL are TRUE or FALSE. Specify FALSE to use the highest level of mathematical rigor in finding any solutions. The default is TRUE. DSOLVE(...,'MaxDegree',n) controls the maximum degree of polynomials for which explicit formulas will be used in SOLVE calls during the computation. n must be a positive integer smaller than 5. The default is 2. DSOLVE(...,'Implicit',true) returns the solution as a vector of equations, relating the dependent and the independent variable. This option is not allowed for systems of differential equations. DSOLVE(...,'ExpansionPoint',a) returns the solution as a series around the expansion point a. DSOLVE(...,'Order',n) returns the solution as a series with order n-1. Examples: % Example 1 syms x(t) a dsolve(diff(x) == -a*x) returns ans = C1/exp(a*t) % Example 2: changing the independent variable x = dsolve(diff(x) == -a*x, x(0) == 1, 's') returns x = 1/exp(a*s) syms x(s) a x = dsolve(diff(x) == -a*x, x(0) == 1) returns x = 1/exp(a*s) % Example 3: solving systems of ODEs syms f(t) g(t) S = dsolve(diff(f) == f + g, diff(g) == -f + g,f(0) == 1,g(0) == 2) returns a structure S with fields S.f = (i + 1/2)/exp(t*(i - 1)) - exp(t*(i + 1))*(i - 1/2) S.g = exp(t*(i + 1))*(i/2 + 1) - (i/2 - 1)/exp(t*(i - 1)) syms f(t) g(t) v = [f;g]; A = [1 1; -1 1]; S = dsolve(diff(v) == A*v, v(0) == [1;2]) returns a structure S with fields S.f = exp(t)*cos(t) + 2*exp(t)*sin(t) S.g = 2*exp(t)*cos(t) - exp(t)*sin(t) % Example 3: using options syms y(t) dsolve(sqrt(diff(y))==y) returns ans = 0 syms y(t) dsolve(sqrt(diff(y))==y, 'IgnoreAnalyticConstraints', false) warns Warning: The solutions are subject to the following conditions: (C67 + t)*(1/(C67 + t)^2)^(1/2) = -1 and returns ans = -1/(C67 + t) % Example 4: Higher order systems syms y(t) a Dy = diff(y); D2y = diff(y,2); dsolve(D2y == -a^2*y, y(0) == 1, Dy(pi/a) == 0) syms w(t) Dw = diff(w); D2w = diff(w,2); w = dsolve(diff(D2w) == -w, w(0)==1, Dw(0)==0, D2w(0)==0) See also SOLVE, SUBS, SYM/DIFF, odeToVectorfield. Documentation for dsolve doc dsolve
