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Solving stiff differential equations


Hi all,

I want to solve the following nonlinear ODE

x'[t] == M - 3 x[t] Sqrt[-M*t + 7/10 + x[t]]

x[0] == 3/10

where M is a very large number (~10^43).

I tried solving this using

M = 10^43;
s = NDSolve[{x'[t] == M - 3 x[t] Sqrt[-M t + 7/10 + x[t]],
   x[0] == 3/10}, x[t], {t, -10, 10}, WorkingPrecision -> 20]
Plot[Evaluate[x[t] /. s], {t, -10, 10}, PlotRange -> All]

but I got a lot of errors.  Could anyone please advise how I should go
about solving this?

Best regards,
James


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