Solving a first order ODE with dsolve

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

Answer 1

[John D'Errico]

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.