Solving ODE with sqrt

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Bart van Dijk
Bart van Dijk on 4 Oct 2021
Answered: Walter Roberson on 4 Oct 2021
I tried to solve an ODE with a square root, but didn't manage. Can someone help me? This is the ODE:

Answers (2)

J Chen
J Chen on 4 Oct 2021
If you know how to solve an ODE in Matab, the problem might be negative values for the sqrt().

Walter Roberson
Walter Roberson on 4 Oct 2021
syms rho g h3 delta p A1 A2
syms h1(t)
lhs = diff(h1);
rhs = sqrt(2 * (rho * g * (h3 - h1) - delta*p)/(rho * (1-(A1/A2)^2)))
rhs(t) = 
eqn = lhs == rhs
eqn(t) = 
sol = simplify(dsolve(eqn))
sol = 
size(sol)
ans = 1×2
2 1
So assuming that none of the variables are implicit functions (such as h3 looks like it might be...), then there are two solutions. One of the two appears to include a boundary condition, but the other does not appear to include a boundary condition, which is a bit puzzling.

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