积分和微分方程的MAPLE求解

符号运算系统MAPLE的使用 (四）
六、积分
七、微分方程（组）的求解
六、积分
不定积分
Int(ln(t)/t,t); int(ln(t)/t,t);
int.mws
> Int(x*sin(x),x)=int(x*sin(x),x); > Int(sin(x)/x,x)=int(sin(x)/x,x);

x e
2 1
2
2 x

dx,

0
sin t dt , t


e
x2
dx
七 微分方程求解
> ?dsolve ode1:=t*diff(y(t),t) =y(t)*ln(t*y(t))-y(t);
> dsolve(ode1,y(t));
ode2:=diff(y(t),t,t)
+2*diff(y(t),t)+3*y(t)=a*sin(t);
> ans1 := combine(dsolve(sys1 union IC_1,{x(t),y(t)}),trig);
> IC_2 := {x(a)=A,diff(x(a),a)=B}; > ans2 := combine(dsolve(sys1 union IC_2,{x(t),y(t)}),trig);
微分方程组求通解
> ######## solve the system of ODES
> sys1:= {diff(y(t),t) =-x(t),diff(x(t),t)=y(t)};
> dsolve(sys1, {x(t),y(t)}); sys2 := {diff(f(x),x) = cos(f(x)), diff(g(x),x) = -f(x)^(1/2), diff(h(x),x,x) = g(x)/f(x)};
>Int(sin(x)/x,x=0..infinity)=int(sin (x)/x,x=0..infinity);
>Int(a*exp(b*x),x=0..d)=int(a*exp(b* x),x=0..d);
求下列积分
x 1 x3 8 dx,
x
2
sin( x a)dx,
sin x x dx,
> dsolve(ode2,y(t));
微分方程的初值问题求解
> ##### solve the initial value problems of ODE > dsolve({ode1, y(1)=a},y(t)); > dsolve({ode2,y(0)=2,D(y)(0)=1}, y(t));
> Int(exp(t)/t,t)=int(exp(t)/t,t);
定积分
Int(exp(-x),x=a..b);
int(exp(-x),x=a..b);
I1:=Int(exp(-x^2),x=0..1)
=int(exp(-x^2),x=0..1);
> ?erf > evalf(I1); ## 求近似值
> dsolve(sys2, {f,g,h});
微分方程组的初值问题求解
> ######### solve the system of ODES with initial value conditions
> IC_1 := {x(a)=A,y(b)=B}; > ans1 := dsolve(sys1 union IC_1,{x(t),y(t)});
课堂练习
1. y xy x e ,
2 2x
yBaidu Nhomakorabea(0) 2;
2. y 3 y 2 y x 2e x ; dx1 dt x2 x1 (0) 1 dx2 3. 4 x1 4 x2 2 x3 , x2 (0) 0 dt x3 (0) 1 dx3 2 x x x 1 2 3 dt