Problems plotting an implicit solution to a differential equation

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Georg
Georg 2025-7-20
评论： Georg 2025-7-20
Ran in:
I am trying to plot the implicit solution to a differential equation, but fimplicit comes up with an error. The code is
clear all
syms y(x)
eqn = diff(y) == (2*x+y+2)/(2*x+y-4);
solutions = dsolve(eqn,Implicit=true)
solutions = 
impl = subs(solutions(1),[sym("C1"),x],[0,x])
impl = 
fimplicit(impl)
Warning: Error in state of SceneNode.
Unable to convert symbolic expression to double array because it contains symbolic function that does not evaluate to number. Input expression must evaluate to number.
The solution to the differential equation is correct. I am afraid I don't understand the error message for fimplicit...

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采纳的回答

Torsten
Torsten 2025-7-20
Ran in:
For more complicated cases where an explicit solution cannot be found:
syms y(x)
eqn = diff(y) == (2*x+y+2)/(2*x+y-4);
solutions = dsolve(eqn,Implicit=true)
solutions = 
syms u
impl1 = subs(lhs(solutions(1))-rhs(solutions(1)),[sym("C1"),y],[0,u]);
[impl2,~] = numden(lhs(solutions(2)));
impl2 = subs(impl2,y,u);
impl1 = matlabFunction(impl1,'Vars',[x,u])
impl1 = function_handle with value:
@(x,u)u-x-log(u+x.*2.0-2.0).*2.0+2.0
impl2 = matlabFunction(impl2,'Vars',[x,u])
impl2 = function_handle with value:
@(x,u)u+x.*2.0-2.0
hold on
fimplicit(impl1)
fimplicit(impl2)
hold off
grid on

更多回答（1 个）

Walter Roberson
Walter Roberson 2025-7-20
Ran in:
syms y(x)
eqn = diff(y) == (2*x+y+2)/(2*x+y-4);
solutions = dsolve(eqn,x)
solutions = 
impl1 = subs(solutions(1),[sym("C1"),x],[0,x])
impl1 = 
●
impl2 = solutions(2)
impl2 = 
fplot([impl1, impl2], [1 3.5])
  1 个评论
Georg
Georg 2025-7-20
The problem with the explicit answer is that it is only plotted up to the point where the tangent becomes vertical. I was suspecting that it continues on, and Torsten's answer above shows that.

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