matlab求（d³y）/dx³+3（dy/dx）+2y=6的通解并求满足y"（0）=1,y´（0）=2,y（0）=3的特解.

matlab求（d³y）/dx³+3（dy/dx）+2y=6的通解并求满足y"（0）=1,y´（0）=2,y（0）=3的特解.
matlab求（d³y）/dx³+3（dy/dx）+2y=6的通解
并求满足y"（0）=1,y´（0）=2,y（0）=3的特解.

matlab求（d³y）/dx³+3（dy/dx）+2y=6的通解并求满足y"（0）=1,y´（0）=2,y（0）=3的特解.
>> dsolve('D3y+3Dy+2y=6','x')
ans =
1/6*x^3+1/2*C1*x^2+C2*x+C3
>> dsolve('D3y+3Dy+2y=6','D2y(0)=1,Dy(0)=2,y(0)=3','x')
ans =
1/6*x^3+1/2*x^2+2*x+3

你这个微分方程不好解。先给你一个实例吧。
比如
>> dsolve(['D3y=6'],'D2y(0)=1','Dy(0)=2','y(0)=3','x')
有结果
ans =
x^3+1/2*x^2+2*x+3
当然上面只是简单的情况
对于你的方程
可以写成：
>> dsolve(['D3y+3*Dy+2*y=6'],'D...

全部展开

你这个微分方程不好解。先给你一个实例吧。
比如
>> dsolve(['D3y=6'],'D2y(0)=1','Dy(0)=2','y(0)=3','x')
有结果
ans =
x^3+1/2*x^2+2*x+3
当然上面只是简单的情况
对于你的方程
可以写成：
>> dsolve(['D3y+3*Dy+2*y=6'],'D2y(0)=1','Dy(0)=2','y(0)=3','x')
得到结果：
ans =
3+1/12*(2^(1/2)+1)^(1/3)*(18-15*2^(1/2)-6*i*3^(1/2)+12*(2^(1/2)+1)^(1/3)-2*i*(2^(1/2)+1)^(2/3)*3^(1/2)-12*(2^(1/2)+1)^(1/3)*2^(1/2)+9*(2^(1/2)+1)^(2/3)*2^(1/2)+6*i*3^(1/2)*(2^(1/2)+1)^(1/3)*2^(1/2)-12*i*3^(1/2)*(2^(1/2)+1)^(1/3)+3*i*(2^(1/2)+1)^(2/3)*3^(1/2)*2^(1/2)-6*(2^(1/2)+1)^(2/3)+5*i*3^(1/2)*2^(1/2))/(-3*(2^(1/2)+1)^(1/3)-i*3^(1/2)*(2^(1/2)+1)^(1/3)-3*2^(1/2)+3+i*3^(1/2)*2^(1/2)-i*3^(1/2))*exp((2^(1/2)+1)^(1/3)*(-1-(2^(1/2)+1)^(1/3)+(2^(1/2)+1)^(1/3)*2^(1/2))*x)+1/6*(2^(1/2)+1)^(2/3)*(6*2^(1/2)-6-3*i*3^(1/2)*(2^(1/2)+1)^(1/3)*2^(1/2)+2*i*3^(1/2)*(2^(1/2)+1)^(1/3)+11*i*(2^(1/2)+1)^(2/3)*3^(1/2)*2^(1/2)-16*i*(2^(1/2)+1)^(2/3)*3^(1/2)-6*i*3^(1/2)+3*i*3^(1/2)*2^(1/2))/(-3*(2^(1/2)+1)^(1/3)-i*3^(1/2)*(2^(1/2)+1)^(1/3)-3*2^(1/2)+3+i*3^(1/2)*2^(1/2)-i*3^(1/2))*exp(-1/2*(2^(1/2)+1)^(1/3)*(-1-(2^(1/2)+1)^(1/3)+(2^(1/2)+1)^(1/3)*2^(1/2)+i*3^(1/2)-i*3^(1/2)*(2^(1/2)+1)^(1/3)+i*3^(1/2)*(2^(1/2)+1)^(1/3)*2^(1/2))*x)+(-1/12*(2^(1/2)+1)^(2/3)-1/6*(2^(1/2)+1)^(1/3)+1/8*(2^(1/2)+1)^(2/3)*2^(1/2)+1/24*(2^(1/2)+1)^(1/3)*2^(1/2)+1/12*i*(2^(1/2)+1)^(2/3)*3^(1/2)-1/6*i*3^(1/2)*(2^(1/2)+1)^(1/3)-1/8*i*(2^(1/2)+1)^(2/3)*3^(1/2)*2^(1/2)+1/24*i*3^(1/2)*(2^(1/2)+1)^(1/3)*2^(1/2))*exp(1/2*(2^(1/2)+1)^(1/3)*(1+(2^(1/2)+1)^(1/3)-(2^(1/2)+1)^(1/3)*2^(1/2)+i*3^(1/2)-i*3^(1/2)*(2^(1/2)+1)^(1/3)+i*3^(1/2)*(2^(1/2)+1)^(1/3)*2^(1/2))*x)
是不是很乱啊。再添一句
vpa(ans,3)
得到
3.+(-.481e-1+.243e-2*i)*exp(-.603*x)+(.281e-1+.551*i)*exp((.302-1.80*i)*x)+(.228e-1-.541*i)*exp((.302+1.80*i)*x)
这个解有复数，比较不好看。

收起