题目

matlab求下列初值问题的解
（1）x^2+2xy-y^2+(y^2+2xy-x^2)*dy/dx=0,y|x=1=1；（2）d2x/d(t^2)+2n*dx/dt+a^2*x=0,x|t=0=x0,dx/dt|t=0=V0

提问时间：2021-12-17

答案

x1=dsolve('(x^2+2*x*y-y^2)+(y^2+2*x*y-x^2)*Dy=0','y(1)=1','x')
x1 =
1/2+1/2*(1+4*x-4*x^2)^(1/2)
x2=dsolve('D2x+2*n*Dx+a^2*x=0','x(0)=x0,Dx(0)=V0','t')
x2 =
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)