数学建模作业求解常微分方程和人口模型问题

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1、word格式姓名胡家炜评分实验报告实验报告课程名称：数学建模课题名称：求解常微分方程与人口模型专业：信息与计算科学姓名：胡家炜班级：123132完成日期：2016年6月10日....word格式一．求解微分方程的通解(1).dsolve('2*x^2*y*Dy=y^2+1','x')ans=(exp(C3-1/x)-1)^(1/2)-(exp(C3-1/x)-1)^(1/2)i-i(2).dsolve('Dy=(y+x)/(y-x)','x')ans=x+2^(1/2)*(x^2+C12)^(1/2)x-2^(1/2)*(x^2+C12)^(1/2)(3).dsolve('Dy

2、=cos(y/x)+y/x','x')ans=(pi*x)/2-x*log(-(exp(C25+log(x))-i)/(exp(C25+log(x))*i-1))*i....word格式(4).dsolve('(x*cos(y)+sin(2*y))*Dy=1','x')ans=-asin(x/2+lambertw(0,-(C30*exp(-x/2-1))/2)+1)(5).dsolve('D2y+3*Dy-y=exp(x)*cos(2*x)','x')ans=C32*exp(x*(13^(1/2)/2-3/2))+C33*exp(-x*(13^(1/2)/2+3/2))+(13

3、^(1/2)*exp(x*(13^(1/2)/2-3/2))*exp((5*x)/2(13^(1/2)*x)/2)*(2*sin(2*x)-cos(2*x)*(13^(1/2)/2-5/2)))/(13*((13^(1/2)/2-5/2)^2+4))-(13^(1/2)*exp(x*(13^(1/2)/2+3/2))*exp((5*x)/2+(13^(1/2)*x)/2)*(2*sin(2*x)+cos(2*x)*(13^(1/2)/2+5/2)))/(13*((13^(1/2)/2+5/2)^2+4))（6）dsolve('D2y+4*y=x+1+sin(x)','x')an

4、s=cos(2*x)*(cos(2*x)/4-sin(2*x)/8+sin(3*x)/12-sin(x)/4+(x*cos(2*x))/4-1/4)+sin(2*x)*(cos(2*x)/8-cos(3*x)/12+sin(2*x)/4+cos(x)/4+(x*sin(2*x))/4....word格式+1/8)+C35*cos(2*x)+C36*sin(2*x)二．求初值问题的解（1）.dsolve('x^2+2*x*y-y^2+(y^2+2*x*y-x^2)*Dy=0','y(1)=1','x')ans=(x*((-4*x^2+4*x+1)/x^2)^(1/2))/2+1/

5、2(2).dsolve('D2x+2*n*Dx+a^2*x=0','x(0)=x0','Dx(0)=V0')ans=(exp(-t*(n-(-(a+n)*(a-n))^(1/2)))*(V0+n*x0+x0*(-(a+n)*(a-n))^(1/2)))/(2*(-(a+n)*(a-n))^(1/2))-(exp(-t*(n+(-(a+n)*(a-n))^(1/2)))*(V0+n*x0-x0*(-(a+n)*(a-n))^(1/2)))/(2*(-(a+n)*(a-n))^(1/2))三．给出函数f(x)=sinx+cosx在x=0点的7阶taylor展开式以及在x=1处的5阶

6、taylor展开式。（1）.symx;taylor(exp(x)*sin(x)+2^x*cos(x),7,0)....word格式ans=(log(2)^2/48-log(2)^4/48+log(2)^6/720-1/80)*x^6+(log(2)/24-log(2)^3/12+log(2)^5/120-1/30)*x^5+(log(2)^4/24-log(2)^2/4+1/24)*x^4+(log(2)^3/6-log(2)/2+1/3)*x^3+(log(2)^2/2+1/2)*x^2+(log(2)+1)*x+1(2).symx;taylor(exp(x)*sin(x)+

7、2^x*cos(x),5,1)ans=2*cos(1)+exp(1)*sin(1)-(x-1)^2*(cos(1)-cos(1)*exp(1)+2*log(2)*sin(1)-cos(1)*log(2)^2)+(x-1)^3*(sin(1)/3+(cos(1)*exp(1))/3-cos(1)*log(2)-(exp(1)*sin(1))/3+(cos(1)*log(2)^3)/3-log(2)^2*sin(1))+(x-1)^4*(cos(1)/12-(exp(1)*sin(1))/6+(