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11-09-2017
Mathematics

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Find the value of kk for which the constant function x(t)=kx(t)=k is a solution of the differential equation 5t3dxdt−5x−4=05t^3dxdt−5x−4=0.

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Аноним Аноним

21-09-2017

The constant solution is
x(t) = k

It satisfies the ODE
[tex]5t^{3} \frac{dx}{dt}-5x-4=0[/tex]

Because x' = 0, therefore
-5k - 4 = 0
k = - 4/5

Answer: [tex]k=- \frac{4}{5} [/tex]

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