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07.第七章用Matlab解常微分方程
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07.第七章用Matlab解常微分方程

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  • 1. 第 7章 用 MATLAB 解常微分方程 利用 dsolve 命令可以很方便的求得常微分方程的通解和满足给定条件的特解。但须注 意在建立方程时 y ′, y′′, y′′′ …应分别输入为 Dy,d2y,d3y…,且一般需要指明自变量。 例 7.7.1 求 2 y′′ + y′ − y = 2e 的通解 x 解 y=dsolve(‘2*D2y+Dy-y=2*exp(x)’,’x’) ↙ y= (exp(x)^2)+c1+c2*exp(1/2*x)*exp(x))/exp(x) pretty(y) ↙ exp( x) 2 + c1 + c 2 exp(1/ 2 x) exp( x) exp( x) 上面 dsolve 命令中的第二个参数‘x’用来指明自变量 x。如果省略该参数,MATLAB 将 以 t 为自变量来给出方程的解  2 2 y dy x e = x3 + 1 例 7.7.2 求初值问题  dx 的解  y (1) = 0  解 dequ=’x^2*exp(2*y)*Dy=x^3+1’ ↙ dequ= x^2*exp(2*y)*Dy=x^3+1 y=dsolove(degu,’y(1)=0’,’x’) ↙ y= 1/2*log((x^3-2+2*x)/x) pretty(y) ↙ x3 − 2 + 2 x 1/2log( ) x