How to solve single non-linear equation?

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ISHA ARORA
ISHA ARORA 2021-9-21
评论： ISHA ARORA 2021-9-24
Can anyone please help in solving the following equation:
d/dt[V.(X/1-X)]= An-Ax-Bx
where, V and X are function of t.
A,B, and n are constants

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Walter Roberson
Walter Roberson 2021-9-21
Ran in:
syms A B n X(t) V(t)
eqn = diff(V(t) .* X(t)/(1-X(t)), t) == A*n - A*X(t) - B*X(t)
eqn = 
SE = simplify(lhs(eqn) - rhs(eqn))
SE = 
collect(SE, X(t))
ans = 
dsolve(ans)
Warning: Unable to find symbolic solution.
ans = [ empty sym ]
You do not have a single linear equation. You are taking the derivative of a multiple of function V and function X and that is something that cannot be resolved by itself.
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Walter Roberson
Walter Roberson 2021-9-22
Ran in:
Please confirm that what you are taking the derivative of on the left side is the product of two unknown functions in t.
If so, then my understanding is the situation cannot be resolved -- in much the same way that you cannot solve a single equation in two variables except potentially down to finding a relationship between the variables.
In some cases it can be resolved. For example, if V(t) is known to be linear
syms A B n X(t) V(t) C2 C1 C0
V(t) = C1*t + C0
V(t) = 
eqn = diff(V(t) .* X(t)/(1-X(t)), t) == A*n - A*X(t) - B*X(t)
eqn = 
SE = simplify(lhs(eqn) - rhs(eqn))
SE = 
col = collect(SE, X(t))
col = 
sol = simplify(dsolve(col))
sol = 
... which is independent of time. Extending V(t) to quadratic gives you a situation dsolve() is not able to resolve.
ISHA ARORA
ISHA ARORA 2021-9-24
Thank you so much Sir. It helped me to solve my problem.

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