why do i receive error when do 'Implicit' solution true?
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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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Walter Roberson
2023년 4월 27일
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
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Walter Roberson
2023년 5월 2일
syms y(x)
eqn=diff(y,x)==3*(x*y)^(1/2);
sol = dsolve(eqn, 'implicit', true)
sol1 = arrayfun(@(X)isolate(X, y), sol);
arrayfun(@(X) sqrt(lhs(X)) == simplify(sqrt(rhs(X)), 'ignoreanalytic', true), sol1)
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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