ex05_solutions

Solutions

Nonlinearity is a typical sign of unsolvability, but here DSolve prevails.

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$(*3.7*)DSolve[{y '[t] + y[t]^20, y[0] 2}, y[t], t] Plot[y[t]/.%, {t, 0, 10}]$

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[Graphics:../HTMLFiles/ex05_solutions_53.gif]

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In the next one, DSolve fails. We will solve it using NDSolve, but to do that, we must supply the problem with some initial conditions. Remember to give the interval to NDSolve!

In[26]:=

(*3.8*)DSolve[{θ''[t] + 1/10θ '[t] + 2Sin[θ[t]] 3Cos[2t]}, &# ... 513;1, θ '[0] 0}, θ[t], {t, 0, 10Pi}] Plot[θ[t]/.%, {t, 0, 10Pi}]

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$DSolve[{2 Sin[θ[t]] + θ^′[t]/10 + θ^′′[t] 3 Cos[2 t]}, θ[t], t]$

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[Graphics:../HTMLFiles/ex05_solutions_58.gif]

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Created by Mathematica (April 10, 2007)