where is the mistake?

Pachito

Hello
everything follows up well, but when I compare the result (eq. 5) with the numerical solution of eq. 1, then are different. Where is the mistake? eq. 3?
thanks

JJacquelin

The mistake is in the integration of eq.[3] because
exp(kt)dx isn't equal to d(x exp(kt) )
So, Eq.[4] is false.
Do not forget that t is function of x.
t(x) is the reciprocal function of x(t)
So you would have to integrate exp(kt(x))dx, not simply exp(kt)dx with t constant.

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Pachito	where is the mistake? Tweet Hello everything follows up well, but when I compare the result (eq. 5) with the numerical solution of eq. 1, then are different. Where is the mistake? eq. 3? thanks Attached Thumbnails

JJacquelin	The mistake is in the integration of eq.[3] because exp(kt)dx isn't equal to d(x exp(kt) ) So, Eq.[4] is false. Do not forget that t is function of x. t(x) is the reciprocal function of x(t) So you would have to integrate exp(kt(x))dx, not simply exp(kt)dx with t constant.