数学实验与数学建模matlab实验报告78.docx

数学实验与数学建模实验报告学院:信息科学与工程学院专业班级:姓名:学号:(1)(2)(3)(xcosy+sin2y)y`=1(4)(5)解:(1)dsolve('Dy=(y+x)/(y-x)','x')(2)dsolve('Dy=cos(y/x)+x/y','x')(3)dsolve('(x*cos(y)+sin(2*y))*Dy=1','x')(4)dsolve('D2y+3*Dy-y=exp(x)*cos(2*x)','x')(5)dsolve('D2y+3*Dy-y=exp(x*cos(2*x))','x')ans=exp(1/2*(-3+13^(1/2))*x)*C2+exp(-1/2*(3+13^(1/2))*x)*C1-1/13*13^(1/2)*(-Int(exp(1/2*x*(3-13^(1/2)+2*cos(2*x))),x)*exp(x*13^(1/2))+Int(exp(1/2*x*(3+13^(1/2)+2*cos(2*x))),x))*exp(-1/2*(3+13^(1/2))*x)(1)(2)解:(1)dsolve('x^2+2*x*y-y^2+(y^2+2*x*y-x^2)*Dy=0','y(1)=1','x')(2)dsolve('D2x+2*n*Dx+a^2*x=0','x(0)=x0','Dx(0)=V0','t')ans=1/2*(n*x0+(n^2-a^2)^(1/2)*x0+V0)/(n^2-a^2)^(1/2)*exp((-n+(n^2-a^2)^(1/2))*t)-1/2*(n*x0-(n^2-a^2)^(1/2)*x0+V0)/(n^2-a^2)^(1/2)*exp((-n-(n^2-a^2)^(1/2))*t):[x,y]=dsolve('Dx+5*x+y=exp(t)','Dy-x-3*y=exp(2*t)','t')x=-4*exp((-1+15^(1/2))*t)*C2+exp((-1+15^(1/2))*t)*C2*15^(1/2)-4*exp(-(1+15^(1/2))*t)*C1-exp(-(1+15^(1/2))*t)*C1*15^(1/2)+2/11*exp(t)+1/6*exp(2*t)y=exp((-1+15^(1/2))*t)*C2+exp(-(1+15^(1/2))*t)*C1-1/11*exp(t)-7/6*exp(2*t)(1)方程组满足的特解。(2)微分方程组在初始条件下的特解.(3):(1)[x,y]=dsolve('Dx=y+1','Dy=x+1','x(0)=-2','y(0)=0','t')(2)[x,y]=dsolve('Dx+x+2*y=exp(t)','Dy-x-y=0','x(0)=1','y(0)=0','t')(3)[x,y]=dsolve('Dx+3*x-y=0','Dy-8*x+y=0','x(0)=1','y(0)=4','t'),为了得到甲板的面积。;然后等间距地测得纵向高度,自左向右分别为:,,,,,,,,,,,计算甲板的面积。解:>>y=[,,,,,,,,,,];>>n=length(y);>>x=linspace(0,,n);>>S1=trapz(x,y)>>pp=spline(x,y);>>S2=quadl(***@ppval,0,,[],[],pp)>>figure('position',[200,150,900,400])>>xx=[x,fliplr([x(1),x,x(end)])];>>yy=[y/2,fliplr([y(1)/2,-y/2,y(end)/2])];>>plot(xx,yy)>>fill(xx,yy,[]),在水平直线上运动。(a);(b)?解:(a)X=0::; F=[20 21 21 20 19    9  0]; Xi=0::; Fi=interp1(X,F,