why do i receive error when do 'Implicit' solution true?

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sedat
sedat 2023-4-27
评论： Walter Roberson 2023-5-2
syms y(x)
eqn=diff(y,x)==3*(x*y)^(1/2);
dsolve(eqn,'Implicit',true)
when i run this code
ans =
y(x) == 0
(y(x)^(3/2)*(C1 + 27*y(x)^(1/2)))^(2/3)/y(x) == (9*x)/((3^(1/2)*1i)/2 + 1/2)^2
(y(x)^(3/2)*(C1 + 27*y(x)^(1/2)))^(2/3)/y(x) == (9*x)/((3^(1/2)*1i)/2 - 1/2)^2
(y(x)^(3/2)*(C1 + 27*y(x)^(1/2)))^(2/3)/y(x) == 9*x
programme prints on the screen this but implicit solution of this diferential equation is x^(3/2)-sqrt(y)=C
if someone can help me it would be great, thanks!!!

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采纳的回答

Walter Roberson
Walter Roberson 2023-4-27
sol = dsolve(eqn, 'implicit', true)
arrayfun(@(X)isolate(X, y), sol)
You will see that they are different ways of writing it. There might potentially be theoretic differences if x or y(x) are negative or complex valued
  2 个评论
sedat
sedat 2023-5-2
thanks for the answer but it still doesn't print x^(3/2)-sqrt(y)=C which is implicit solution of the problem.
Walter Roberson
Walter Roberson 2023-5-2
Ran in:
syms y(x)
eqn=diff(y,x)==3*(x*y)^(1/2);
sol = dsolve(eqn, 'implicit', true)
sol = 
sol1 = arrayfun(@(X)isolate(X, y), sol);
arrayfun(@(X) sqrt(lhs(X)) == simplify(sqrt(rhs(X)), 'ignoreanalytic', true), sol1)
ans = 
Notice that analytic constraints had to be ignored. You would have to prove that your version is valid for negative x.

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