Question

用matlab求微分方程2(x/y^3)dx+[(y-3x^2)/y^4]dy=0的通解

用matlab

Answer 1

m文件如下：

fun_u=@(x,y) -2*x*y^4/(y^3*(y-3*x^2));

[x,y]=ode45(fun_u, 0:0.1:20, 1);

[x,y]

plot(x,y);

xlabel('x');

ylabel('y');

y=dsolve('Dy=-2*x*y^4/(y^3*(y-3*x^2))','x')

结果：

 

y =

 

      0

  2*x^2

 x^2*z1

z1 = RootOf(z^3 - z*exp(2*C9 - 4*log(x)) + 2*exp(2*C9 - 4*log(x)), z)