# Solving a first order ODE with dsolve

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GuoZheng Lee 2021 年 3 月 25 日

Hi I wanted to use matlab to solve a bernoulli equation: using dsolve
This is the answer from matlab:
>> syms y(x)
>> ODE = diff(y, x) - 5*y == -5/2*y^3
ODE(x) =
diff(y(x), x) - 5*y(x) == -(5*y(x)^3)/2
>> y = dsolve(ODE)
y =
2^(1/2)*(-1/(exp(C1 - 10*x) - 1))^(1/2)
0
2^(1/2)
-2^(1/2)
The answer from matlab is different from the hand calculated solution: .
May I know how to get matlab to show the above answer? Also, what is the 3 numbers below the answer (0, 2^(1/2), -2^(1/2)) for? Thank you

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### 採用された回答

John D'Errico 2021 年 3 月 25 日

While you may THINK that is the only answer, is it true that y==0 is also a solution?
How about the constant value of sqrt(2)? -sqrt(2)?
So is it vaguely possible that your hand calculated solution is not a complete one?
Next, consider that any expression can be writtten in different, but valid ways. Consider the expression:
exp(C + x)
where C is some unknown constant. Can that also be written as
D*exp(x)
where D is some equally unknown constant?
Since you did not provide initial values of any sort to dsolve, it produces a valid solution. The solution may not look exactly like yours, but it is still a valid solution, and in fact, a more complete solution than what you found.

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